1Oct 29shy350 PM

Transformations of graphs

To explore geometrical transformations and their effects on the graphs of functions

To relate transformations with the variations in the equation of a function

General objectives

2Oct 29shy350 PM

Transformations of graphs

To explore vertical and horizontal translations and their effects on the graphs of functions

To relate translations with the variations in the equation of a function

TRANSLATIONS

Lesson 1

3Oct 29shy350 PM

Based on the graph of f(x) draw the graph of f(x)+3

4Oct 29shy350 PM

What will the graph of f(x) shy 2 be Vertical translationggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

2Oct 29shy350 PM

Transformations of graphs

To explore vertical and horizontal translations and their effects on the graphs of functions

To relate translations with the variations in the equation of a function

TRANSLATIONS

Lesson 1

3Oct 29shy350 PM

Based on the graph of f(x) draw the graph of f(x)+3

4Oct 29shy350 PM

What will the graph of f(x) shy 2 be Vertical translationggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

3Oct 29shy350 PM

Based on the graph of f(x) draw the graph of f(x)+3

4Oct 29shy350 PM

What will the graph of f(x) shy 2 be Vertical translationggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

4Oct 29shy350 PM

What will the graph of f(x) shy 2 be Vertical translationggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

5Oct 29shy350 PM

Based on the graph of f(x) draw the graph of f(x) shy 1

y=f(x)

6Oct 29shy350 PM

This is the graph of y = f(x) Sketch the graph off(x) shy 4 y=f(x)

7Oct 29shy350 PM

Conclusions If y = f (x)

y = f (x ) + c translates vertically the graph of y = f (x) c units

bull If it moves upwards

bull If it moves downwards

c gt 0

c lt 0

translation vector

8Oct 29shy350 PM

Based on the graph of draw the graph of y = f (x shy 2)

f(xshy2)=

y=f(x)

If find f (x shy 2)

9Oct 29shy350 PM

Based on the graph of draw the graph of y=f(xshy2)

f(xshy2)=

y=f(x)

Horizontal translationggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

6Oct 29shy350 PM

This is the graph of y = f(x) Sketch the graph off(x) shy 4 y=f(x)

7Oct 29shy350 PM

Conclusions If y = f (x)

y = f (x ) + c translates vertically the graph of y = f (x) c units

bull If it moves upwards

bull If it moves downwards

c gt 0

c lt 0

translation vector

8Oct 29shy350 PM

Based on the graph of draw the graph of y = f (x shy 2)

f(xshy2)=

y=f(x)

If find f (x shy 2)

9Oct 29shy350 PM

Based on the graph of draw the graph of y=f(xshy2)

f(xshy2)=

y=f(x)

Horizontal translationggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

7Oct 29shy350 PM

Conclusions If y = f (x)

y = f (x ) + c translates vertically the graph of y = f (x) c units

bull If it moves upwards

bull If it moves downwards

c gt 0

c lt 0

translation vector

8Oct 29shy350 PM

Based on the graph of draw the graph of y = f (x shy 2)

f(xshy2)=

y=f(x)

If find f (x shy 2)

9Oct 29shy350 PM

Based on the graph of draw the graph of y=f(xshy2)

f(xshy2)=

y=f(x)

Horizontal translationggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

8Oct 29shy350 PM

Based on the graph of draw the graph of y = f (x shy 2)

f(xshy2)=

y=f(x)

If find f (x shy 2)

9Oct 29shy350 PM

Based on the graph of draw the graph of y=f(xshy2)

f(xshy2)=

y=f(x)

Horizontal translationggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

9Oct 29shy350 PM

Based on the graph of draw the graph of y=f(xshy2)

f(xshy2)=

y=f(x)

Horizontal translationggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

10Oct 29shy350 PM

y=f(x)

Use your GDC to draw the graph of and

11Oct 29shy350 PM

y=f(x)

andCompare

What can you predict about the graph of g

12Oct 29shy350 PM

asymptotes

13Oct 29shy350 PM

Conclusions

y= f( x shy b)

y= f( x + b)

y= f( x )If

b gt0

translates horizontally the graph of y= f( x ) b units to the right

translates horizontally the graph of y= f( x ) b units to the left

translation vector

translation vector

14Oct 29shy350 PM

Exercise 1 Sketch the graph of f(x) shy 2 f (x shy 3)

f(x)

15Oct 29shy350 PM

Exercise 2 Sketch the graph of the function Hence sketch the graph of

16Oct 29shy350 PM

Exercise 3 bull Sketch the graph of bull Sketch the graph of bull Find g(x) in its simplest form

17Oct 29shy350 PM

Exercise 4bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

18Oct 29shy350 PM

Exercise 5bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

19Oct 29shy350 PM

Lesson 2

Given sketch the graphs of the following functions on the

same set of axes

20Oct 29shy350 PM

Transformations of graphs

To explore stretches and reflections and their effects on the graphs of functions

To relate stretches and reflections with the variations in the equation of a function

STRETCH

Lesson 2

REFLECTIONS

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

11Oct 29shy350 PM

y=f(x)

andCompare

What can you predict about the graph of g

12Oct 29shy350 PM

asymptotes

13Oct 29shy350 PM

Conclusions

y= f( x shy b)

y= f( x + b)

y= f( x )If

b gt0

translates horizontally the graph of y= f( x ) b units to the right

translates horizontally the graph of y= f( x ) b units to the left

translation vector

translation vector

14Oct 29shy350 PM

Exercise 1 Sketch the graph of f(x) shy 2 f (x shy 3)

f(x)

15Oct 29shy350 PM

Exercise 2 Sketch the graph of the function Hence sketch the graph of

16Oct 29shy350 PM

Exercise 3 bull Sketch the graph of bull Sketch the graph of bull Find g(x) in its simplest form

17Oct 29shy350 PM

Exercise 4bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

18Oct 29shy350 PM

Exercise 5bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

19Oct 29shy350 PM

Lesson 2

Given sketch the graphs of the following functions on the

same set of axes

20Oct 29shy350 PM

Transformations of graphs

To explore stretches and reflections and their effects on the graphs of functions

To relate stretches and reflections with the variations in the equation of a function

STRETCH

Lesson 2

REFLECTIONS

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

12Oct 29shy350 PM

asymptotes

13Oct 29shy350 PM

Conclusions

y= f( x shy b)

y= f( x + b)

y= f( x )If

b gt0

translates horizontally the graph of y= f( x ) b units to the right

translates horizontally the graph of y= f( x ) b units to the left

translation vector

translation vector

14Oct 29shy350 PM

Exercise 1 Sketch the graph of f(x) shy 2 f (x shy 3)

f(x)

15Oct 29shy350 PM

Exercise 2 Sketch the graph of the function Hence sketch the graph of

16Oct 29shy350 PM

Exercise 3 bull Sketch the graph of bull Sketch the graph of bull Find g(x) in its simplest form

17Oct 29shy350 PM

Exercise 4bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

18Oct 29shy350 PM

Exercise 5bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

19Oct 29shy350 PM

Lesson 2

Given sketch the graphs of the following functions on the

same set of axes

20Oct 29shy350 PM

Transformations of graphs

To explore stretches and reflections and their effects on the graphs of functions

To relate stretches and reflections with the variations in the equation of a function

STRETCH

Lesson 2

REFLECTIONS

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

13Oct 29shy350 PM

Conclusions

y= f( x shy b)

y= f( x + b)

y= f( x )If

b gt0

translates horizontally the graph of y= f( x ) b units to the right

translates horizontally the graph of y= f( x ) b units to the left

translation vector

translation vector

14Oct 29shy350 PM

Exercise 1 Sketch the graph of f(x) shy 2 f (x shy 3)

f(x)

15Oct 29shy350 PM

Exercise 2 Sketch the graph of the function Hence sketch the graph of

16Oct 29shy350 PM

Exercise 3 bull Sketch the graph of bull Sketch the graph of bull Find g(x) in its simplest form

17Oct 29shy350 PM

Exercise 4bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

18Oct 29shy350 PM

Exercise 5bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

19Oct 29shy350 PM

Lesson 2

Given sketch the graphs of the following functions on the

same set of axes

20Oct 29shy350 PM

Transformations of graphs

To explore stretches and reflections and their effects on the graphs of functions

To relate stretches and reflections with the variations in the equation of a function

STRETCH

Lesson 2

REFLECTIONS

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

14Oct 29shy350 PM

Exercise 1 Sketch the graph of f(x) shy 2 f (x shy 3)

f(x)

15Oct 29shy350 PM

Exercise 2 Sketch the graph of the function Hence sketch the graph of

16Oct 29shy350 PM

Exercise 3 bull Sketch the graph of bull Sketch the graph of bull Find g(x) in its simplest form

17Oct 29shy350 PM

Exercise 4bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

18Oct 29shy350 PM

Exercise 5bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

19Oct 29shy350 PM

Lesson 2

Given sketch the graphs of the following functions on the

same set of axes

20Oct 29shy350 PM

Transformations of graphs

To explore stretches and reflections and their effects on the graphs of functions

To relate stretches and reflections with the variations in the equation of a function

STRETCH

Lesson 2

REFLECTIONS

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

15Oct 29shy350 PM

Exercise 2 Sketch the graph of the function Hence sketch the graph of

16Oct 29shy350 PM

Exercise 3 bull Sketch the graph of bull Sketch the graph of bull Find g(x) in its simplest form

17Oct 29shy350 PM

Exercise 4bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

18Oct 29shy350 PM

Exercise 5bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

19Oct 29shy350 PM

Lesson 2

Given sketch the graphs of the following functions on the

same set of axes

20Oct 29shy350 PM

Transformations of graphs

To explore stretches and reflections and their effects on the graphs of functions

To relate stretches and reflections with the variations in the equation of a function

STRETCH

Lesson 2

REFLECTIONS

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

16Oct 29shy350 PM

Exercise 3 bull Sketch the graph of bull Sketch the graph of bull Find g(x) in its simplest form

17Oct 29shy350 PM

Exercise 4bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

18Oct 29shy350 PM

Exercise 5bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

19Oct 29shy350 PM

Lesson 2

Given sketch the graphs of the following functions on the

same set of axes

20Oct 29shy350 PM

Transformations of graphs

To explore stretches and reflections and their effects on the graphs of functions

To relate stretches and reflections with the variations in the equation of a function

STRETCH

Lesson 2

REFLECTIONS

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

17Oct 29shy350 PM

Exercise 4bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

18Oct 29shy350 PM

Exercise 5bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

19Oct 29shy350 PM

Lesson 2

Given sketch the graphs of the following functions on the

same set of axes

20Oct 29shy350 PM

Transformations of graphs

To explore stretches and reflections and their effects on the graphs of functions

To relate stretches and reflections with the variations in the equation of a function

STRETCH

Lesson 2

REFLECTIONS

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

18Oct 29shy350 PM

Exercise 5bull Sketch the graph of and indicate clearly any asymptotebull Sketch the graph of and indicate clearly any asymptote

19Oct 29shy350 PM

Lesson 2

Given sketch the graphs of the following functions on the

same set of axes

20Oct 29shy350 PM

Transformations of graphs

To explore stretches and reflections and their effects on the graphs of functions

To relate stretches and reflections with the variations in the equation of a function

STRETCH

Lesson 2

REFLECTIONS

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

19Oct 29shy350 PM

Lesson 2

Given sketch the graphs of the following functions on the

same set of axes

20Oct 29shy350 PM

Transformations of graphs

To explore stretches and reflections and their effects on the graphs of functions

To relate stretches and reflections with the variations in the equation of a function

STRETCH

Lesson 2

REFLECTIONS

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

20Oct 29shy350 PM

Transformations of graphs

To explore stretches and reflections and their effects on the graphs of functions

To relate stretches and reflections with the variations in the equation of a function

STRETCH

Lesson 2

REFLECTIONS

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

21Oct 29shy350 PM

What is the effect on the graph of that will produce if

y= f(x)y= a f(x)

a

Set up your GDC in degrees

Prepare domain

With your calculator plot the graphs of

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

22Oct 29shy350 PM

y = sin x

Vertical stretchggb

geogebra_thumbnailpng

geogebra_javascriptjs

function ggbOnInit()

geogebraxml

23Oct 29shy350 PM

Verify your conclusion for the graphs of

24Oct 29shy350 PM

Conclusions

y= a f( x )

y= f( x )If

a gt1

stretches vertically the graph of y= f( x ) scale factor

stretches vertically the graph of y= f( x ) scale factor

a

y= f( x )1a

1a

25Oct 29shy350 PM

Use your calculator to draw the graph of for

On the same grid draw What effect produces the 2 of f(2x) on the graph of f(x)

26Oct 29shy350 PM

y= sin (2x) horizontal stretch scale factor

y= sin x y= sin (2x)

Now draw and

Horizontal stretchggb

geogebra_thumbnailpng

geogebraxml

24Oct 29shy350 PM

Conclusions

y= a f( x )

y= f( x )If

a gt1

stretches vertically the graph of y= f( x ) scale factor

stretches vertically the graph of y= f( x ) scale factor

a

y= f( x )1a

1a

25Oct 29shy350 PM

Use your calculator to draw the graph of for

On the same grid draw What effect produces the 2 of f(2x) on the graph of f(x)

26Oct 29shy350 PM

y= sin (2x) horizontal stretch scale factor

y= sin x y= sin (2x)

Now draw and

Horizontal stretchggb

geogebra_thumbnailpng

geogebraxml

25Oct 29shy350 PM

Use your calculator to draw the graph of for

On the same grid draw What effect produces the 2 of f(2x) on the graph of f(x)

26Oct 29shy350 PM

y= sin (2x) horizontal stretch scale factor

y= sin x y= sin (2x)

Now draw and

Horizontal stretchggb

geogebra_thumbnailpng

geogebraxml

26Oct 29shy350 PM

y= sin (2x) horizontal stretch scale factor

y= sin x y= sin (2x)

Now draw and

Horizontal stretchggb

geogebra_thumbnailpng

geogebraxml

27Oct 29shy350 PM

y= sin (frac12x) horizontal stretch scale factor 2

y= sin x y= sin (frac12x)

28Oct 29shy350 PM

Conclusions y= f( x )If

a gt1

y= f( ax ) stretches horizontally the graph of y= f( x ) scale factor 1

a

y= f( x )1a stretches horizontally the graph of

y= f( x ) scale factor a

29Oct 29shy350 PM

Exercise 1bull The function f is defined by

bull Sketch the function with the help of your GDCbull Describe the geometric transformation that will apply to the graph of f

30Oct 29shy350 PM

Use your calculator to draw the graphs of and

What geometrical transformation does -f(x) represent

31Oct 29shy350 PM

Based on the graph of y= f(x) draw the graph of y = shy f(x)

32Oct 29shy350 PM

Write down the equations of both lines

33Oct 29shy350 PM

Reflect the following function about the y-axis

34Oct 29shy350 PM

Completeg(2) = f () g(1) = f () g(shy1) = f ()

g(shy2) = f () g(x) = f ()

y = f(x)y =g(x)

35Oct 29shy350 PM

Conclusions

y = shyf( x )

y= f(shy x )

y= f( x )If

reflects the graph of y= f( x ) about the x-axis

reflects the graph of y= f( x ) about the y-axis

36Oct 29shy350 PM

f(x)

f(xshy2)

f(x)+3

2f(x)

Match graphs and formulae

37Oct 29shy350 PM

f(x)

f(x)+ab f(x)+c b f(x)

f(x+a)

38Oct 29shy350 PM

y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

28Oct 29shy350 PM

Conclusions y= f( x )If

a gt1

y= f( ax ) stretches horizontally the graph of y= f( x ) scale factor 1

a

y= f( x )1a stretches horizontally the graph of

y= f( x ) scale factor a

29Oct 29shy350 PM

Exercise 1bull The function f is defined by

bull Sketch the function with the help of your GDCbull Describe the geometric transformation that will apply to the graph of f

30Oct 29shy350 PM

Use your calculator to draw the graphs of and

What geometrical transformation does -f(x) represent

31Oct 29shy350 PM

Based on the graph of y= f(x) draw the graph of y = shy f(x)

32Oct 29shy350 PM

Write down the equations of both lines

33Oct 29shy350 PM

Reflect the following function about the y-axis

34Oct 29shy350 PM

Completeg(2) = f () g(1) = f () g(shy1) = f ()

g(shy2) = f () g(x) = f ()

y = f(x)y =g(x)

35Oct 29shy350 PM

Conclusions

y = shyf( x )

y= f(shy x )

y= f( x )If

reflects the graph of y= f( x ) about the x-axis

reflects the graph of y= f( x ) about the y-axis

36Oct 29shy350 PM

f(x)

f(xshy2)

f(x)+3

2f(x)

Match graphs and formulae

37Oct 29shy350 PM

f(x)

f(x)+ab f(x)+c b f(x)

f(x+a)

38Oct 29shy350 PM

y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

29Oct 29shy350 PM

Exercise 1bull The function f is defined by

bull Sketch the function with the help of your GDCbull Describe the geometric transformation that will apply to the graph of f

30Oct 29shy350 PM

Use your calculator to draw the graphs of and

What geometrical transformation does -f(x) represent

31Oct 29shy350 PM

Based on the graph of y= f(x) draw the graph of y = shy f(x)

32Oct 29shy350 PM

Write down the equations of both lines

33Oct 29shy350 PM

Reflect the following function about the y-axis

34Oct 29shy350 PM

Completeg(2) = f () g(1) = f () g(shy1) = f ()

g(shy2) = f () g(x) = f ()

y = f(x)y =g(x)

35Oct 29shy350 PM

Conclusions

y = shyf( x )

y= f(shy x )

y= f( x )If

reflects the graph of y= f( x ) about the x-axis

reflects the graph of y= f( x ) about the y-axis

36Oct 29shy350 PM

f(x)

f(xshy2)

f(x)+3

2f(x)

Match graphs and formulae

37Oct 29shy350 PM

f(x)

f(x)+ab f(x)+c b f(x)

f(x+a)

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y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

30Oct 29shy350 PM

Use your calculator to draw the graphs of and

What geometrical transformation does -f(x) represent

31Oct 29shy350 PM

Based on the graph of y= f(x) draw the graph of y = shy f(x)

32Oct 29shy350 PM

Write down the equations of both lines

33Oct 29shy350 PM

Reflect the following function about the y-axis

34Oct 29shy350 PM

Completeg(2) = f () g(1) = f () g(shy1) = f ()

g(shy2) = f () g(x) = f ()

y = f(x)y =g(x)

35Oct 29shy350 PM

Conclusions

y = shyf( x )

y= f(shy x )

y= f( x )If

reflects the graph of y= f( x ) about the x-axis

reflects the graph of y= f( x ) about the y-axis

36Oct 29shy350 PM

f(x)

f(xshy2)

f(x)+3

2f(x)

Match graphs and formulae

37Oct 29shy350 PM

f(x)

f(x)+ab f(x)+c b f(x)

f(x+a)

38Oct 29shy350 PM

y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

31Oct 29shy350 PM

Based on the graph of y= f(x) draw the graph of y = shy f(x)

32Oct 29shy350 PM

Write down the equations of both lines

33Oct 29shy350 PM

Reflect the following function about the y-axis

34Oct 29shy350 PM

Completeg(2) = f () g(1) = f () g(shy1) = f ()

g(shy2) = f () g(x) = f ()

y = f(x)y =g(x)

35Oct 29shy350 PM

Conclusions

y = shyf( x )

y= f(shy x )

y= f( x )If

reflects the graph of y= f( x ) about the x-axis

reflects the graph of y= f( x ) about the y-axis

36Oct 29shy350 PM

f(x)

f(xshy2)

f(x)+3

2f(x)

Match graphs and formulae

37Oct 29shy350 PM

f(x)

f(x)+ab f(x)+c b f(x)

f(x+a)

38Oct 29shy350 PM

y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

32Oct 29shy350 PM

Write down the equations of both lines

33Oct 29shy350 PM

Reflect the following function about the y-axis

34Oct 29shy350 PM

Completeg(2) = f () g(1) = f () g(shy1) = f ()

g(shy2) = f () g(x) = f ()

y = f(x)y =g(x)

35Oct 29shy350 PM

Conclusions

y = shyf( x )

y= f(shy x )

y= f( x )If

reflects the graph of y= f( x ) about the x-axis

reflects the graph of y= f( x ) about the y-axis

36Oct 29shy350 PM

f(x)

f(xshy2)

f(x)+3

2f(x)

Match graphs and formulae

37Oct 29shy350 PM

f(x)

f(x)+ab f(x)+c b f(x)

f(x+a)

38Oct 29shy350 PM

y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

33Oct 29shy350 PM

Reflect the following function about the y-axis

34Oct 29shy350 PM

Completeg(2) = f () g(1) = f () g(shy1) = f ()

g(shy2) = f () g(x) = f ()

y = f(x)y =g(x)

35Oct 29shy350 PM

Conclusions

y = shyf( x )

y= f(shy x )

y= f( x )If

reflects the graph of y= f( x ) about the x-axis

reflects the graph of y= f( x ) about the y-axis

36Oct 29shy350 PM

f(x)

f(xshy2)

f(x)+3

2f(x)

Match graphs and formulae

37Oct 29shy350 PM

f(x)

f(x)+ab f(x)+c b f(x)

f(x+a)

38Oct 29shy350 PM

y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

34Oct 29shy350 PM

Completeg(2) = f () g(1) = f () g(shy1) = f ()

g(shy2) = f () g(x) = f ()

y = f(x)y =g(x)

35Oct 29shy350 PM

Conclusions

y = shyf( x )

y= f(shy x )

y= f( x )If

reflects the graph of y= f( x ) about the x-axis

reflects the graph of y= f( x ) about the y-axis

36Oct 29shy350 PM

f(x)

f(xshy2)

f(x)+3

2f(x)

Match graphs and formulae

37Oct 29shy350 PM

f(x)

f(x)+ab f(x)+c b f(x)

f(x+a)

38Oct 29shy350 PM

y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

35Oct 29shy350 PM

Conclusions

y = shyf( x )

y= f(shy x )

y= f( x )If

reflects the graph of y= f( x ) about the x-axis

reflects the graph of y= f( x ) about the y-axis

36Oct 29shy350 PM

f(x)

f(xshy2)

f(x)+3

2f(x)

Match graphs and formulae

37Oct 29shy350 PM

f(x)

f(x)+ab f(x)+c b f(x)

f(x+a)

38Oct 29shy350 PM

y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

36Oct 29shy350 PM

f(x)

f(xshy2)

f(x)+3

2f(x)

Match graphs and formulae

37Oct 29shy350 PM

f(x)

f(x)+ab f(x)+c b f(x)

f(x+a)

38Oct 29shy350 PM

y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

( Content-type applicationmathematica )1313( Wolfram Notebook File )13( httpwwwwolframcomnb )1313( CreatedBy=Mathematica 60 )1313(CacheID 234)13( Internal cache information13NotebookFileLineBreakTest13NotebookFileLineBreakTest13NotebookDataPosition[ 145 7]13NotebookDataLength[ 60740 1231]13NotebookOptionsPosition[ 33699 647]13NotebookOutlinePosition[ 60142 1216]13CellTagsIndexPosition[ 60031 1210]13WindowFrame-gtNormal13ContainsDynamic-gtTrue )1313( Beginning of Notebook Content )13Notebook[13Cell[BoxData[13 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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

37Oct 29shy350 PM

f(x)

f(x)+ab f(x)+c b f(x)

f(x+a)

38Oct 29shy350 PM

y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

( Content-type applicationmathematica )1313( Wolfram Notebook File )13( httpwwwwolframcomnb )1313( CreatedBy=Mathematica 60 )1313(CacheID 234)13( Internal cache information13NotebookFileLineBreakTest13NotebookFileLineBreakTest13NotebookDataPosition[ 145 7]13NotebookDataLength[ 60740 1231]13NotebookOptionsPosition[ 33699 647]13NotebookOutlinePosition[ 60142 1216]13CellTagsIndexPosition[ 60031 1210]13WindowFrame-gtNormal13ContainsDynamic-gtTrue )1313( Beginning of Notebook Content )13Notebook[13Cell[BoxData[13 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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

38Oct 29shy350 PM

y = f(x)

y = a f(x)

y = f(ax)

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

( Content-type applicationmathematica )1313( Wolfram Notebook File )13( httpwwwwolframcomnb )1313( CreatedBy=Mathematica 60 )1313(CacheID 234)13( Internal cache information13NotebookFileLineBreakTest13NotebookFileLineBreakTest13NotebookDataPosition[ 145 7]13NotebookDataLength[ 60740 1231]13NotebookOptionsPosition[ 33699 647]13NotebookOutlinePosition[ 60142 1216]13CellTagsIndexPosition[ 60031 1210]13WindowFrame-gtNormal13ContainsDynamic-gtTrue )1313( Beginning of Notebook Content )13Notebook[13Cell[BoxData[13 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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

39Oct 29shy350 PM

Translations

vertical translation

horizontal translation

Stretchs

vertical stretch (a)

horizontal stretch ( )

Reflections

reflection x-axis

reflection y-axis

c

ALibraryOfFunctionsWithTransformationsnbp

( Content-type applicationmathematica )1313( Wolfram Notebook File )13( httpwwwwolframcomnb )1313( CreatedBy=Mathematica 60 )1313(CacheID 234)13( Internal cache information13NotebookFileLineBreakTest13NotebookFileLineBreakTest13NotebookDataPosition[ 145 7]13NotebookDataLength[ 60740 1231]13NotebookOptionsPosition[ 33699 647]13NotebookOutlinePosition[ 60142 1216]13CellTagsIndexPosition[ 60031 1210]13WindowFrame-gtNormal13ContainsDynamic-gtTrue )1313( Beginning of Notebook Content )13Notebook[13Cell[BoxData[13 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t7TjpN8r6DSr9SjSZFKUi60nEFYUbgqcahMRKKoEt13gscXxdtBPf6qsgl43FCLM4bH9WlBHnV2kj2UV0+Qfq5Uqqfr3u5TXqL3kf13oUdKTYe+yimUNum9wxGYpHBmzbON4Xhe+3p5S360hbd5HQvXGrqx66NjmR137AL8pPetZwuPY9FY++D3kc5ypUEFPo5OXChrNsBdZc26K71xVRVjSunDB2x13dNXObKabmsLpcJpLHduK2R1biymIS63PeOFFTYrgN8+M45kPzkxaxn6KM71304Fnz+eJy4qM329rHwA9J8Pvcc31rlzkTdr1dNdFwC5MxNC5y5AWtOgUTbD13Ofg9UI5xbXIInt2bYXdlnfDmNgQybV3mE8EdTZ1v9x83u6v2XujOR7erUM5p1377TzUebyrJOXd5T3xXHX9kldqhgbvrAnalDE1N7mZmZe3D4Un+GLSBnuPIJ13PWO7Y3OFtyf3dV7NbR3ICF7Lm5zcf6ILf4YRTVToDCOXxfFoyCzd2a9MVv8o13UkZIcAXwpeHs3w4fp6cOu6mugZyPr69j8gT5HzqggLogdsXuRTytgIBZEvA13jPHcsVu7QUPrUOYNuHGmYOTWnrogfX8FDDdu7wWke3x3ezj7XG9m71huZK4A13brdTeiiQaerbDsof3j3UMbTDNZD98e39xHdh60QAYnPPHx6E7rRf2+EZ2oHj13M5gTmznSPZ7HqbHQmJkjD+4fcF9FN6qbE3tiM4XdYzuY62sb2BGdOwym1slJ13sVrD2ZLxARxDMB4GHJpGU2fB+H3yKMW9yXlSekd3g04pzVcQeWY7Qwgipf135tyk4E2ivAof3DvkHcqBMYSuIWFFvBkowauzhWAAzZH+dCgDJvrZg8M91eA13hW2DmYNju3EQaLqJ4iu4fcw9XEHTF9wZCfPKBLh2fOgBNXA5n46j6l34H13aUUrWtGKVrSiFa1oRSu0kaRfsArJo1yS6FyksNqEedfvAmqUuG2uE2rdFWd13v9eWbD+baoe7Sjxhj2zfcDyFSnxVdfXwXss5QRWaislT6XKn6zWs2G4ut3V132LNGXFCD8WOSakO09fGtY8mniS1D2TvoJfHuUXEPejuVduJCayKm75W2pSO137lKxyLOFxxWt+mqXgCF+zemAW11vkPSwrXJCyBc0pxe0pgG+MwnE0glTbVX13ozuWsbRFV9KoI3epWFvXxddho9p54LvsPcURvO16I83biu+rGfG6XzoPbgF13FJa36ADHFqJROb0VBRu26eeeTgLuGfpx8ZVtvzirbnr6Ox2PyTydIrGIfI135kVJP8YSOnUlTdCXbaGxkmg01jVeCqaWt6Vj0OLFNHLJilzq+UtMluXRybGf13osWddfL89tNn951yHWwI7D7ds7vF9a3p8j8+Kdfbe36s5Oh3FO+eeuvOUp13yrlk3XsmuJeSLwkWyitloXcgEiwzRtHdzvg6yOEye27R3fFZgufTx+50pdF13+box3OzJw8P37+1zBEyUEcvE3lnoPuQzdYuQTcnpKekN0l0tnBq6g05nlTo13GttJldE8vgMD6cOgvITPQZQVePTW4Li1J39sdmCEyEzfMG1DSLh0z2200bv13BJjlpt4MpmswZ5TXTDySCdP1k6pnD4+Qvyg2dGfqUGT2aJ1Xzz5jXaO50LWW13gWyKScf1gyzczNGOwSzMsREOMfbtaz5WNZKC5yFzB5OT+GpB5kWHK3aF136r2K9oDB01MHXzwsaOjG8G2wweJLvzexH25xYFyk0YmDWdA9nFfXKdQHMD9b13S38W81cYZw2N+kT6hwz0X50m4x1BJXZbWudgQxtRdl0jeRiWSN4dCiAgeMN13muQAASdDp+ZomXx2z+XdB22EGDg+yuVz858QaM2+lQBtSb+jNjc4U9oztr136JliJzT34A70VCSnMjJYelFMn14bvrA6S5KTYY24zg4guiMDUP6fO4IjAnF13LQoUt7iJz7uGa7iGa7iGa7iGa7iGv454lQczAzMOlRqPJFPdKdZ6JBIGZKo713JadElrfLMiviUAE97CAE9ThcifXziHJdrPZiJhlZjyzvXycu6V9sa+PwVPan13wC3exfhKOT5utbiST8y2mEMs0Z516Oe6HDPIsZymJetEyktWs5iv7KXwVPo313D1kJQjfuPxjyfWPL40XtKWMp79tcctqvjQ1eEbNs4J61NpFx5baA7ehGUt13xuNX9HXORxk98mL2ebwd6tc+tJmAFUaX3X62KxyPMXj58uPCnFBFb641fS13rT+FbtRNfb9VSVmzUL+qvjKtsB4Gfo+Peg7dmlbSZP+XPBdZqswHVYrJrAq13uvQ1Rs4F3wEQHbfa0kEhRhVuwRMikX5r0Dt5HQA0JF7zqLLaT+kH7O9w5813vP0oBIbBLUhtaZFYgvIX2EqLUxyVdyo6xovjcSi8Jf4MXQhK7ry9SjxY5d613hP6d3l0zDnAgFiDOSfb9jjL8lqLci62vN3c8+2OS3yuOJfPfvJr7af+daV134J9cuPInT8xDH+Yfsnz7YZQjs2fafebHSGzBbPf48PYivGD+T2jzBdRhje13sXcMI90mJwwnGIM3Xxh99hOB6XbsgTYmxS9nqw+Qc4Btw5w9lWv+RlGsX413wf0Kf9U3gvxVS38W8k5+XWz+6M0J9DuqCeA5jZAFtIpc4cbwxl1QbEFPYUK13ZHtwruHGyOyR3uu7oF5DucrrQpgEzBEU5x4cjM0U4ErwojAyNvOFVV6jhei1130PBODCQczEHuqNMAMj2jO2Kz+Y3hTPxuDQiOgKl9UHLuqgtKuaTA1Kk7B2q813JqR6QgLyaTNIJeE6DBois0ev396Hnm9+6Z0MpsZmjjYNZIFJTL51jWKadH4v13NfdnIP1FleYOx3NxiGtD4hz0wdA2BZI5K+gMHVPZLLeQ6ltjoxaNSKydhz13QGff+E7CDdR3MDvxu19lBsNZxbA3uG82MwR6D7INPcRCzcGCvG1PzF54NnD13I9XEQfGi8FEwNcodBDXw2zhAPKHONEWXzoMnfR9AXM9khubK2wNb8fB8XC013o+EVvG81XMM1XMM1XMM1XMM1DXCUFXaj4K6lWE29eDG1DLz1lYp32mq413ZYN4qmX4q03FVecFbInna6PwrcY7fVr8Fa9SVV1dNgC302F2FgoerHDqipvS13PEMfxqKxuaeTA7esw3culLemUa71tOLL+tknd6LRaGisbO7xnZa+1HenF7S13nBa8Xi4xTnSYIOZ4d+rgUlPPd9HhKhorbUoHteeC71MKrEgZe3ORTvbIutT713Lh8LWNGGOPtHVTp1dJJgenUHqm3sx6TXU3d6Xoctp53dAbOJRkDLAG8qd1320qb9JLjVpuODygsb9F3jSKH1n29rELKxAVN61gPNFrt1tdRDm2O1IMH6lRo139nL+cMTBv9wbz1f9poOHQU8tvLvziVplOY6+37458aZH3zJf+rIxf6C1304GdJ4M7z4b2nfLudPhzHAETxcchpdMznstn81G2cOQl5qYPROcKGvsyYKgH13xpCicQ1ks0yDF5246oIGPu2uZ4TzX2UqXpTwEeMHfZJfJQUYFnD8IDEzhd3X13c+0hIzNIloDeGc6OzB7tG98FrbcN7IzNFYOb+cc43bploKe0R1IU9MtDnQb1327w7qHoXP7ox7t4VQA+ObEP7ESCiPJEIS02cxTzbrGHp19s6s+MzBXcvrVf13PjNRaBvKoYP58hwcpAGzxy9O3kQ5SklF8Uz5mN4o09oH8iVgLkBGJE+MRm133sTQvKDBGeZkWTiYbBUzWhS4R49VEOzMALHpqYOAj328R17ecYtciR9kfNE313NYhUElyNcP4rCiqsC4pNsjz6UNGJkNaAvpUiMXuv78JuUsqsbgzSRMcw6MXk13JAV40jGR7EYFt8AY9ozuBEkwm0cM85XhPBrYEmVI7fQY2jf0udZwDddwDddw13DddwDdfwzxCeEMOVLI4vRSaKNeFaOBa9SslIXgzVVlRv5LcT7Uels6UFj+413BfGtY8mniwsbt06S4HyeXW2nvsqlL2vFYMB781djkWj4puOk961Pnj8ta9aV13Nacfv6K0vWfmaeydhwY+tg+cMtahvzV10NjJeSU9aSibVulU1flFPDMweb013xu7yn5cJY3sf4UeU9FoFF2hKJVWSaMuGkWPqYvd75W16iucBlKYznnYK1r113xF8Zqyl1fJlLZ3MfHL1z7tnz2aGJM56hH0OjUw8lgpulImpCBrcYiSqKp3513q67xUhRoTYNLoJTvFpedfiMdp8pvpgpiOQ5QiYTgSzTvXkNvYV+k5+aa713v7kv2L+dJtWD5QsTy5ecM3HPnt53za3MfX7Q998bA396rvWb568U13+E5ktrXknQjl1gUwMbgzjNnRiSqR4sptPkwh3j+aG310lB2TkICSU6bHZvOj13ckLc4cilOTKERQ5f3vrYDafuAdQezu5Bs2KYe50DuWSwGGOYBwOF7f2B6K13TJRi3p2D25Uc6ez0ze+k+cdZNgjS0pXHhSv9Geg29VsfgRJmAMnuk3Sq8Mn13TE29QUnXpbMO4ZbI7FFot46zLPqQ7uujhmc5u8fHry+Kzy2a+zmroXZo2j13eShD4ITmy+cmNqPrmhgoZ8SXsE4jO+xy1nQob8oHDTg8YhBkRmqvhF0GGsP1354BV4TH0jGIqidy3cBiZum8MZ87dOxKbPwqNTk7uVZLPJ6xwifUiuokzt5On13E6UcpFRXmLNrRCLuoK32sJQ3XuHNbAHyZJs5QqnXRSkLehuu89YFzLF5g5D13RygTlHKoo+TG5nPb+nf0Te+C+aX2EgDeehJh0VywgGmIlsGsrj7dlVqzc17133jVcwzVcwzVcwzVcwzX8NcQ1mq9+Kvir1ZZ1qg5TrR+Kuth28dSz5NXOVf13pgQihuI13gMmKS9I72yzVDcqKtzHkSXqVik3l14AomtnIOfXDsgu7nF772138f02wGcbTneuK2l77uPnkwWXzb+4kpakDgiTEXVgomnKp2Yw6rosoTDf0WX13vlbSmHY28GdKGBZc3rRla8fu5DGyNnAn0PThOuOXdompclqTi9p0pe1bKts1331btEkqbDUVNaQBWt2a19n4w93QiEluYetRT2pQGysta9VCJSvxVemnLNjAe13bRgriuJ5heVQBPgEjcajUYbe9+tcumtnZknvNtPe3af6Nx31pN0fnHlzu133en+b9c+rfRvmIse+Eqn457ETvxWxDRD78Y+eCfPf3bL0wc0w3XLz513szqLzZcuHTgTNd+TIRFrA55N2H8ILvTKCd6uKuiM0dvXEbjxHsGc+NzRaO133djbO5bXO7obPobHdsVmjty5+0at39g9nBd7dLQN+SuiFoMCxR5K8YNIf43s13iswedQ3kOPzClYGcyPzhnpE9joAJ7q3xYQLwFiJkukdyMRXUCanfqojeyxe13obGfKKDxPXWdhjMh07OHeMLg1Zv7LvVk8esLPfG8JkdQhEbhEvoYB03QOzRs13rhD9voKGanktgc6L3Zlw6ebEluT+8gPKp9cqsw1Xoyh43MJ6zoFXm8u8lwK13juy0hkTO5d5zdRePFR7U6zERm5QfGt0NH1vD26meB2Y7fGboQmM4E93JKNf613mZAAxmPa9hu7LnZnV3npNEY6h1fxR+U4dM76Pvfg8OTtAxOTB8I39jT2ZUA313+UWNwYCzeEQj+zCjOAONGxkF8YnBjC5GRjW2pcJw949jsm4GvuyOIcY9BEe13H5jNuQcHYRB6hOg74BP3jkMGtoGdvBhkc19mUwDWjzo98vfldAQxgOFrQO13ZFk8kk+1fDbxJj7vGq7hGq7hGq7hGq7hGv564ZVuAd9wgWowN6N64zb5XrS13OMHV4RgyL+Noa7glXSSF7elilsUqzp1UGc9iL+deKSfrBBpb9WjptjnM8i13XzPuWcwrxfanwrndtcYnynO0WjxBTX69SG36nXSfUG4an0bwa+FeL+Ng4313EA51UVXLOBrihc7PchPLOVLn11u67CaSy+ss0z+KNYNDb75HYx8T99N6031377p+fmFbdct+dotyhj8obtpW0fa1Zy+eNHjeOta47aT3LaahMI+6C2P3iDvS133SC+6+7s8PHLaWUt2y50vQsfo9FoWbOBeSqFvzrjf4dyWKEP1S8ufp35JYfn13AICAVLULle3p1c5sz9CPy5rSylpR5rzvUg0dudRX0lzGpSyVn1JYxoltgIz139CVN+mOX0qEJ5tCCo6VQ54jF4xeFKHmRXQ7eXW74URH5kVn9qWLuRdqcztq13dt+syxi360Ztuunq341UN8viv9N5NhvvKj5N8ty7y888vOBXnv1n3613gyNfg3wtUZl1xvnunebQtlWv1Crd9YHxCZKukZ3UmheRgtaAkYOQ9VdC513auoNu98MMpG5go6h7eQFhKsC3t5w1+jNvQ60D2GEWetA8gmWb3owUUheIv5132zHAcL6QBHDNgPCtiTeorrdQHirmTJoGMDeXk+wJX8vlodqfAama0CJxWPs13GsZc8cTJICVF0XP4boFXOvJXE2AvZjLER23DF0j6CzUN5oD1uKRlJ3o8WUN13iZiHyq3DdeU3EjlWQE5K5lrkjjDDFfQalMBzDV1whjH7FnJrtM7BzvFbe7mO13OaM6jd3onFbQ0pNV3SkSf3W4e2Q7fCVx3vWmPjMPL9zC+bi6x3eTzcZatwGM13gQFc+p7nSZm9f+j25L5HdfHHhXEZijIkXX244B8fHufArlFaAtUAKjev3j13fxegikAY5C+my0AVdD35rB0ZCHq94iTdw4+vHsIvneqMI89tgs2R+YKL3ab132d9sYHwvn7coxftLPJsRxgHnejAHBtzilX5LbLXfSxqu4Rqu4Rqu4Rqu4Rr+136eKr5K8qCbevB9crBXU1fyV0hbc+Ar4K4WP2hh8kRNbgb9KyoNVpeDTFLzG13k5w3k+dOkOfUuLweNQ4VBU+lR7VO4nih15GgkpSXmij8M3jrzg2inH2WtmC13vNOnwl+xBrkIchE3Cqz4bNGydIxQv0LVYNDbwsb3CaShtSTpQZ8LGJ13cg9iUqxnz2fxQECnrsxpPieE8RAprRFNEoFI3FWvq+W9lmwMMKWX2Tonv138o38qLxFX96kOxd8XaPMpS1bCtpTi+mVO18mAJxveh1VpUzr5X0WuP3DC13jaeDb58IHKrq0A3fOQcKmrKzRX1pzeNvC30VhkePJMlVOARsvbkODicMVz13wXf4VET4e3u6C7Dr91xwtbT56wDaPPukRruVec123ms8GdZ9z7Llw61Fmd13d++jP3jx0y9Eir8Qqft8pPJXI8eGPlf+eLfhi7B9Z+Gffi32o9+OeOv13ffKzzwdsey53fvt01x5HCDWQxyNyLJL1Xgevf9xnB1+LEyhTGAmKMOpELJV13I7f2sB9OXVDwjWwHxDeCsWlwb2T2SMYbjulkDrRbYrNHX08cRkVwa88M313kLe5HM7k5Fp47t70oRPdGTbpvEJx6u6eyEzByS5TXdCAXNl8vy9QpsUo2cI13DaP7FlJMQTpAcLbAFd6BB+0F8Gw+h8ySQUHq9lCPnwQLmH84EzBPLQVzEJv13IoqDawxnSivKbwRrg1d3xeYOQ3eU7kcwsu8AfwNapJhBPJ+Rm7t9+DC9OET133VKjdXR4YnQuH4y3StGCBXMP8kHYEtCDbcFrecRZ5YE8JY8qcIaRx7MRecjf13F0sfGSkmcXwXfVGaGsynjw8xI5PVp6amSPRuYJLVl2PjUyIPJRjCd6DOxP13awkJE1NIfJ1EUwU5fnAvD9S1cZyRc90ZDimHlQij9OT+QeqR8GTm8PyDgzBB13cMkRNMqOymgYzDXocQ1kUw464xKn3E153jVcwzVcwzVcwzVcwzX8dcOx8irj13BnfeW2cEUUVZxefslV1SzCFqlXgjuDGxPFtVPzgUmvXhK9YVnmjFj+4jPxW13xbeOJZ8uHlc25L0k45hYvrYTefgKF+aGavC+zRTQ6cBblS4jJjxv0s09nXD113fzDdAKujEyer3LpK9sMZe3G9sEPnj6exHMDWw1nAt98tvB4pOpuo6ssla913pSNnaiYQjcam56+VudIqWXlTYbzoe9IgYGUvz180wYN0YmBLxDG4w7nHZ79134Vt2Jr5u3G99uIJKHkembd6c62dOXNPJxOj1rcWQ3eQnroFM6+D3qjp013lS79pZ73b9x3svHPX8zdnx9xDfzN6MQlpqqmZ4dB5fCdC86hD6bnRjFb18Iz13DNryGyjPdkZDiDJfhfY1fXujWNZz7r0bq+2LVjFi+fcvulfLnzvVxaO13eHz6j8pEGIHfvC3Z+vtv9P1p6Rc6PCJrmyksCgdk42ZjdlC5K+ClEgq13qKOs3YIPPW3yh67vshOF0juGH7vGd7QN7IBLLx4dmX2QfyaESvpHcxdmjz6e13Phi8lts2mPnx7f2xmcL5hwehAh8Dw3nPHh599vAwEV9IN3HG+Id3D7muZjvD13Wbdu7Y3NF2IC+YC5wSe2DGVCQ88fHr45sR9sc1d8ezhEZC1I9819ke9ICa13vruvY2hH62BO71jeFcCDBtdATs49rkH+ZxsCrpzvicTkzXNHYbbn9wCOCZ13Pkw73zu6e3Jyv390p7NO3Tk2aODz6ePnAghoRca2dEshdaf3z3CNhDnJXQ13MpQj5+ZC3zNKhJ4ffcN99VcMODmrb3R2TfJfQsG0wxXIzMFTx8eBbw1nA3G13L0wfhuFt7MuAUT3XmxmbKZDuHcgC8xr7zJxJ3hIgPt8n5blCJ7S5Qs4Djz5j13wQz03Zo5MnRjNJXAxmR+fynj47AKA3e2NlCnm9MeU1PHfQMwRzl3L69D8yG13qeFpxVxYc0dh+sBImIKTXSYYlodTb3iu5sCNH0sibAwPdSBYUxHdvuQbAf13rsIowSRe7M6EAZm4+wY0Pfzx3r6RndAK+pgFDZv5vGu4hmu4hmu4hmu4hmv413a4wrmb0TUoVLHEsIaN6UxmfCXyJs8ibk8kQ1bCYkEzvrt2ah5X7ldcXl513ad79iWJJ+c9lcBvnc06GL5VXtxuPsUU61BMYX8qfG3zsmH8Zyr8JfKqra+e13qixb+o1IG4SL7qx56Im4FavkbOmV7UZShq39V23R2OR+UuVDp1pS3pJU3G138hZdz8fWmcd3YnSU4NnQNyhTejoI1Hv3RmOxBu+bZS70yDrpfv2dNfzyJOp13R13zn9wFPWP3zts7t5c06UFzWbPubOgdCgxcKKeTAYuufP2M731mtDqufngm138N7Fvj+2P0XVycuvnj+OBaNWd3Z9x5fA4Hp+WsO746SNl2Nc0fvjdKFyNNo13FBmuuWf3at14amF5a5p75O9u3G9GplbiMUc7dkjkxefLTxmm4enzpY26dsG13vz3dIKZMfjTfvW7GDTXYYzzYSIZ3r3dIT+sqvkwCc+b3oSfOL6rTIPxB139H99OfLBP184oXt+ybRg+eqLosfKf69jprdF07ln3EWnPbub+jcYfVhBnj013v6Iz9eghNdf60YHH4RfGbqGnU2h4F3ouwRQHxUHKghWbPUQuRgcb+7N5xjE813kNyKHj84sjCTvzCL5ed6DLCX8wTPpvfPpIB3EdGO7nQ5+9wHDuc8oEFZk913GpspHLq+y+LV13gFh9APEznte2TkwfgUnQOs4tTridzlRddT4PX8p5NF0KL13C3NgCaa3qnGbgiM7KRU5mJcPl0CDM5xNnEB2Z6Mh1MH4WpzH56p1zqQNX8f13rYrOvokduV9woSuLSZgJaBFunzscmSuIzuVDuzg+aE8+qKLOmqs7RO9QDlJq130Mqjo7H5I9fGd9l8uDgtbh0Le4d2TE7sg9tRydyb3VdzrSHMgl7ZKfiuYsel13xOkzBXQ2oghrm2LJyWKgF6HLDZPbwbLvH6v9KLcYgwJvCxsRcJwPbB7dcn139oKe4MguPhQO5j7yfQhzGw9yYMbPYdnr3gnKxpScrgrOch88a+gmbLoez13YRwAhC6AcHhsT41HZw+a6oJojGco99kDzDNGefsLe6vaqEjDjGBP2XyhxIc133t7gE6nvGW8a7iGa7iGa7iGa7iGahnAZfimiTWNFhgI9xOMmrcahXtUu513XilO0LhUz7J4XLwhn8qUJA4xhfxa9St40v5uAB5IYX8SXK8ag8YMlxozqf13mKJHPY+p8oFz7shqf7l8MV4TCyI+8UEZxfS2nXRjhUlJjEBFyJtUyFwz5I13wWHjrOgBHD4ubRcqip0gI+F+sZpjIYnUWoonkaf8YDJuXCUu2SnHXcLWbK3513zVLii3X1OKTELd7FeFWKPRSWx1PHjSbHl9Ev1yWc2UgFh48KDuNT4xWUuE6W13YS+dteIb9z5M5K+sfqPVayx1GTlVGmLbu7xZCwWG7htw3zpLbqStrTyNv2p13gJTe6v78SE2HvsSpL2nTVbn0FU7dvbmxq7cvYHKqdkOpc1tlm+F899uXw+9d136Hmv3nsIHZw8YkmrsZiSVp3r+nNmq0BneRsG9388rapR12xaOyU771jjZg713CSUNRuKW9Mv978Pq73UqTfW5DMA9GptKlB1OrvTqw4WLvuw7fEYvHWOfV13l7dDScfoY7cBDLjS5xKXMLVR3bz3ec67n7Rq3qdiZBuaBMed63rzQ+06913bz+FrOI4VHrSrej4JNZ4TXZv1llfqWL3x48Zn720WFPvpy5Adfiv797z23137Yj+9Ncipb+zcPJrC3VfWaj44txHX5z+yZfHfvZHncezL1j2njqt759lyOY13TfGDeHwenjcXMmEkrM90rtccncPz6U52ZVAedQNHyJ7sQr6rSWaubP50Dl6j137wikSloGtjf2oaOUBZZowHSpPwfkMa+7F0MLQazWb6z2GRwBEzpi9WWCqhO913InMmNT6Dza+X1jnlsGrsF5t60XPJHsLXOyzyyk4d9V1o6s1q7DE3dBnpvYf513EH1OTeyExBZafA+ZrghQyvX6TTQ+K5riyrTlO1Jym1wDmZcHMio9abjG13GZoAthnQaKmjzAMd3sbwz1csxVhf88VOum9Rk0tA7mNPbm1PmwIVj2J5n13dylQAnUYh9ZwttUPlScCx2+dCoxL5YAY9LYkwn2oJ1kP9mA41DhSaw6JlU13DF3NxVcQRfC1DexYIMP4PV9F71VQeyKUUR8Q2Ye50mMCU1sGslz9WTDUYAaN13pwCDU+7VQR3fjR3Gqs506CyOuVtpje7pTrTMhUJcfagyocN0861HGuezMa130IMLTYU+do0ihwl4hQf6S55joS33e0nDNVzDNVzDNVzDNVzDP11czUdBHYoN139w5GCSd5BV8qn5RHWgav6NBxaotV81Qbw19tFk7js0r+Cvk64lVWhyfXA3OX13CllPn1lnPcvuNfAfQTiSirhHVlI3w1PNUq8QQebBk7GVf4JWmv9Gr5qXw13VBvEX62Vj9okfEV+bKP4q4SyYX6n6NeHibZqOvS17UgonfG9HYtEY9HYmdA313kEymdVXdYapy6R8nYpGo6HrP6tBhyXknzGK0Kkb+tj64vkTa2cWLWDMmYYz135cfBsfp0dT4DTrrbAMLlLTqMH8SDDWPVzvQqpxFKmctwV5bLBa72P1eZau+13qk0Hb1qwp8ajQ3rNg0RNnQTmIMq+Gsjj6NanxlaoYoIrRAoUjFaPPq6ToFO13u9NZOjPgI2iweOkv3NKJ3ko1mGDNZPUZ+IC+pA0yPX+rIuBCvnvznwkf7J1333Wiw9feHT9efP8LC+W6T668Gav97YXqbQu1wosfffFqqbm94VvNjjeb136g811b8BpfFk3unLOxo6c1zhHZF5PMzOEjKQv6XpfI+ZTuXjoDl8linFt8h13HeRGhWmRvCZ7MMMSQHIGwYDeGhL5obZTJjQ7pdKCuyjlO04f3GUNpNtJmF8R13TNqAgByxTmcgUgdxGfgw3TpLonk+AYmsgAH089uPc6RDvS6kcjFian90bkC13h+wASTmyuBWkp1iPql0Dpy6HSw5aWrzAYrOFmLWengjmwdASSsZll4eiwWsm13O2XPQ8ppz05xePyf2kHax4iU6UvyXJUHRPW8YJ2+dvESJlGfOdI3toe6ifTR13zVv7YvOFME3SM8Lpp+B2vx70r8xKaF8UpgkYrcrt0n1FPrHLnPIwN9oVxn132LQlYCSF6HrH7nYWHgFiFHlwwIze0d2R2aOtAxkqL1ndhjvGq7hGq7hGq7h13Gq7hGv6ZwpOBKjzxrpXkf2lwv5g8Z5EvyaCtV9G4Cu3K65K3p8opl4h9o3G13UdL2eksGfkluDoA9iXn3R6PJLP5fCXiB98GTxVUeSXiRqOn7vkj4N9YKn13LbMe1okjm0H8lcVjrHIK9b59Dx8P4mAsdi5rrcsHn11p7GuE4+Zq+nQD03a13MC7Pvx0QkLd4hWp3eo1LNz51LhpdGLl7qd6Xa+k0Wb1mDLv2ITdi9TLvhAfD13Vbr0Fa60893vc9xflWsbgDUdxqoOXXP4u5jjffijCqehymmsbtfVuAVoxRrQ13szcOck1+oyVAWf29BjYbiQuni5xtn8z9YVOAQABrJjYQ4YEkPXC95IPLDTy137eg+hG5ylHg8kFEf2H42cKSpIXyh795++Ol3xHx7w28+7vfWj7r0Y13OJCyZeel1G7MNfXjH34j8zy0H9vREf6L8+EDZv2nubd757z9nQnpPB13nQ1BE2f2npo62DO6Mzy2C7NXYVjfkbGP98kPOPJFDiSLkOtgfoMdh5T5Ij5K13Mgx7hESKWbrXb2ZJO1JGxDgRT8JvY3Tu8hGXFTTZiYRhgojIIh3faAkY62U13Ct6vZzaJGSGbzGraiW+Bdp3hrNGbe5lNqgsakPICM4gcw49ELhFlRCyZygyp13O8TLBYZze8bzOBUVD3Xi3m0Nd21AWZblrsOxhmV1gy4oVAoJbukhI8koX813j0HMlcH4EF9HNsu8X31AVJ5c5vEwafz80fGP90CPOoayb028EZ3LX3hw9Fyv13GROUQXeoXzSeBroRxsHMhln9gsI0MqMFH6EX3WM7KM77KpnlteSJcSPrYGo13QrrFRzaH9A4Sk06cpDDSM73Zg+N5FDoqSS6lrLfc7yUN13AN13AN13AN13AN1331q4vI+I7h+cnA1whPUcRUGYU+NaZ36V4nMBnib9aFlbevil5a+WkX8113NUGnouagHP8YJnLcDL41uRM7+TD4NSjnomH3XdnuoYnHGUd+iqn0eJFjya71392D7tb+t86F8VTuG6Vk8Rrjl9nQX3DL1KHRvtudU6M2qdt6qGynWTE+RbsZS13Zrx5vQql9438mM+WLDGjQ5+eNpgq66mwzh859z9x0MW11731b+dmuu+cb8d13TIJ2YRwq3WK1O51ZArC5woOBWhx7Rf6ooj2YUe7WVXrSOdcQ4hirJXIfwVSM13BfOba9wm9TmzlVLdXIXxg6Z6f9aJ1rwL1t1tZZmtl7t7H7P3Xd22VZj3413r5EvzFb+7UP3FWOVXHviK3fqtPuevPjr32psOaJ0C6r34ST5RM413vs+GnA+mbIrMHsVkR8RcPZ4+1DuWJ3kc+c2OQIaycpDrCOoox7vZGjLV+XV413J9PWvPMxXHfyZHxPSO1S8oODueIQHl18tnXOLtUKnx6dkdCPnJTh2vT85513ZZV9NaH7MGjwscIHY6unwwfRQbTcjVRVXVCEOkwB0lZ+I82FnmkZEIaPFN9n13WDzP1w8VEe5lFgjHv4O9iXASYZrsQaKSZvMn7xykEYB79RU0XxxvCOuHSCT013WyafUmTYYIXAR+K7xIoOdMwjIssM90JbOP5BzGNW5TFZ0GnNWNapJuxL+QX13rXdhHvg5kMGMSXXo4L7U0fOU7Akx1Jz4gf9de2GykeEHWSfyxSeRw7yUwd131Bt7sqOzhZOTB2AAYU3aaLJgQGBY5OdLD6rIn02gdUt40FDeKcAQsQzYCebV13B5CehYGqcOM8bujzruEaruEaruEaruEaruGfBby8HVOp8CaRcqfo+VjA8nYj134iQPdcCTyktxhSifqEfBlXhDRd6Bv72TxC3aU8Qzfuo47wGXxXUKLu1fVONM13eT82ax7j4jE3QL++2q1X4ZIfwvJ6uL9QUe+L14or8YNL5ZV2lfhBMECJH1y013R44fZHwx3nAZvFOnwg2rxNm2GjmvC+6FU+NKPB3j7AaWEvcs5pvi+MpUOOvf13qLjFVHFa5VPqQfrehnXK3nC14qr14P6uVs7noK6tCXudLq3GKt21DWqitx13pZMnlZHehxyyZ6ygM5sPqHOJ4J8hSut1o8UVpkLU1RZSaLl7gCF57lZw8w13J2AkJyiUqWhLH5qwP194yunT6zoxQLK4XQevRTj8hj6btXHONl6LHZvfrCk13A8bBbPfpiSfhZxOfR+Qr6AA45NDcUuxYlYfePz545yBhVd0hLj67nTsY4hy13ELn17NzCzxTq9BtrPDqY7hO+rDOt2x2uXSf8+037DrVnXep8xvXP9LPfvTl13Xkt28Ow3pypJ3L8y4M1mZ0tf9FfsXvq+7rrcg9Gyh0+Myc5wqdoIhTOtFl13bOnPag1vbxvIaR3IOh+iwDR25qFe8PyyG5U9wOy0mUkSijuTvH2YsJJ9wyg13nIMEcaj9JnZVsoeIXfShMPpE+SjGlnx4YAZ5HVpDuCAxFxa1XkP5ptj1C+aI13eC1B4YWYz6Fxg3k01QUNFZ50fM8EKVdYZzpyg35jfchUybmweI156P1J3al213S993OM4dpgoPRdj59dIc+Y2Ndl37uzrGd3JQXmVxEli3nJan1C4+J7WJT413McRFZQ0wDjYTL2SAeQflFW5RsUF5h2M4qsdwssvUOpBxpSf7cm+mM5x1ti8L13lNRQfH72q2jdpE+qpTWLU4Z1OXvO+ZO9TzO8C49H8qcmNp9cbuqnaB+D1+131nAobDJ3h88afbfSWhWZ+5LzDKCnHNyL8rQkYCLgo51cvDbueddwDddwDddw13DddwDdfwzwKu4p3EeN5pRf4qQT4lruav1Hrw97BPsKl5MxnbPBXjHOKhLz13ieni2l12vipT8FQV9Opq+evVrdOPjX+ahk8WbsJduplO+N4LYV3UssrBXs130V4Bf5WAKxVcnzx3hX4q6Q8WFUK3qwqBd9VvRLvpNYDFUXPp8VfJZQN8Tk13UC8OvkOvKjzGToStX4DH2nHQU8Wvwlj7vAkVnQxsvuMUryez8QJqer8Olun13SJmp9Bypx3PETBF5EJkwRNFrqHVjudDzjcDNH7EfF5RaJNDMFg8O2qnAwcDN13f2oJycpNAvcBpt9kmT4sUwuEyiFKSGSEAKv5LqEtVjlwupHvNHHxHPJK0132DiJutVvquKcoQyHSEzPB0NPvFUz94rl96+9M6Lbvbuz8dnvvdprcp4W13fd5Td6h14M8u+99qOfnHfcfNFy8eOhPaKWWU4sxRUpojfFrt0lCLOIaykZho13PWCyhhaPEKV07oqwVFHupY5TEGWQ8q4HDHLcnBR5p2SUwpEPSItHGgopK5SZ13e2qloZP7LsrDIjn7OYIqL82gRO6hHxchDmmg2GCB+8jJzGlgEaczAQX1wLLB13GMRH1nIydikoL7QY8IhTGdArZjBulwcHl1+IgjiBgoH0yIfTFzcF89rwRi13Avl2qVFqCEkDtiUF4CUsItb9BmVEeC7pKs02qoTYJmQXFxvDrAmqV596v913MGk1YpIxCmKVFcqLVp5u0sbk1dKndQv4J2u4hmu4hmu4hmu4hmv41sHllB3013Uc4XpPy2VP8WTSKrJ7Fdu3BdeJx9ifr1HLyG4Srf42rf8bLu9TE8VkmkGot13+KbMbwo87uoy45wgpmwz1XdtFJ66X2IKOxfx+HWVBEsyCrwuF12UExmf0o813RXj8TXGDy61dkPwVCWpfPzcpVxm6hm0rxOPazHJInkpXCTCQeTANC5W3Ly13MoO0nLzNL2bfVgkooxoK0WemTEU6DRgzisvCzNRKWU6WmWpIxJSeQT8MQ513Uq9MIouyLvQc6LDs7Dy960pv4emeXWf79neceaT0i+02Mv9h5s6M4+233413cssh96Xd5wO7baFMpj7kvEyGFCvh1ZSk61B+scj5xpOt59TvYZWSxPFfcsvm13rE8N13AN13AN13AN13AN1BfdnypzIp6lt9PUUph47rt2RBcvT2RTFLhiv1q13O1Pv+17WHvtSPH5vvjo9qeRXhauKmFCxJ+LCunE1TbSyBKeTXHGsMavH+mj137NOyIh5vT7Ilmqx8KnjKefcnEjgr4EFxzfaslRddf3+XY6Ht8StkGby83VjW13Lq0QqJR3SJc2Eu+QfBplXFhRXsFZZhkcYwxdBs6aDhXAmbxS2gW8xKmHS0Rz13GZfTvwp7Fu3vECrkWDb2I2UHGLV46KfYUCglPXmE6GMsx17WyuPOND9yoK13Y8xu7PiP94v+qPlE4dnQPsw3FTKf6tpxwb3rnDe3PpiJ7jpE4rGPkJxSHkvS13J3GVRXZmW1pncgdMTfIdYtX4PxXtiR+fSoRilmOaVqeIfS3GFav9bgfNK13qeZFtKlwR1Bc7XxpuIZvVTzZOtfWs4ZruIZruIZruIZmniptJCn+68b+J013uGUqnGVYvkyqC0nwdl08LqwGh95S3Gl3TL1vm8tuHoftxzeoVfjyfet6v2g13nAt3tbhKT3k7HXFFOPwsZIoglTxslBZN3ZgDl7esq0eVRAsdM4A8h1woX413uMX4OMpNxjlutELKf4J4pSpHShI8kEI+FZ5CD7ebJP5xjTjrr4zLx7Wh+JJ9139GrwxbxexEXA3lyW16v1qBFPXCvGk+qR81vrAdXxUXWekSqi9zuIi5zCwm413ci+x5TntEzmDTYSV70H4t4bqeWV5zfpe6ZMvnfpe1itZykfYg+Kip6kfMiK139ijvE3rnLL4rFP6K452TrQcDzFFD1ZL7dtPduZZgzlWvwnzSnnN50Nvjn6Y13ecV25HRon9WXYQ3oKbYxq8GLaawozE3gc1ftclSm7fXnrxLeY8nmfaX1sNnr13VsM1fBPwZfirLWWnhmu4hmu4hmu4hv+S4KUqPor5K45RKluCszL4El5MNj713LJVnO2Xeaf240m4cruLTUvFXZerfaWo8lfwaebC4eUm+39Gr+SjJN2PVuIpP130zNnJeHtUg6orcZfJc0ZvMb19luKh5M5otS8VFbBV8Xf5WYH2wt8lUeIRWP13oeKjkvNjSXE7nVmQir9SeINUPFUqXF3scnldcGu8C+gK8nI8muJH6kjMerQO13exLaFRNvkRoV+QRDPIvQl9UQyoGmHZxiPWg6233QXb7rvO3A2e43WJhzLlHa13KFlhfGz10rl7JUVM1vriCKgHKkFmQ+IHN2K+NFzDNVzDNVzDNVzDNVzDNTwR13XyqzNe185XiyfcpG6V9PvpRU8qvCVUVMqNgTceEV4euMU1tru2vVv0Vwkf1Y13Vo0nWVQrtPu6xQa1CxQPOyUbgtvnXHkrx8avmlWdGWeX6t8Q5ICfrjhoUI138KTyL9evpfxVKtD5q9slDYcWSk6QrFOIdyCptNdu06f3nvKtvt0z15FucNv13QO+soHSjTc74cvMX23S+tRwDX+VuLaeNVzDNVzDNVzDNXyr4bb4+tKyVP4z13iceNj39xC7NRvcSL2n8VWD1EkqO1eyf+N5mE3BU09T0n10SnyT8+DL4x13FXZ0njnJX6YL4unindeSV7GhWXwUqgvK580njq5FrsR19Tl45fWVApb9cz13vySd90oyfJ4p24D+eO50xms7jZWd0oxUd4oOaGK3tONew8Ecit8xl5jmr913BorXw+WnTl+1eIH1X6AeM6pdOapqI6jVJ8bqx4f9Tm5ycY5bvxVfsUrzZeG13ahWxtf6tFwDddwDddwDddwDd9MvMRpgI82+kfz4jYd1Dl+sLQtEedtyFKc139cC+bHkcfs+nki+R668GX2Zfmer3WzwurIjbku5U+x31Pm4eI4I1y3Kt0v1139eFK3i0A4aNN0m+ocOrsKhm+FyqVLinGkPdrm4JLub+Ww3FsZjR6XHqJJP13hcfpkeIKWLS+ER7irjFV4bzGkjA5T31YhyfIyimwjcvDpHX9kbGM7qlGFs113byDlGVNwWSYVXkrP2tLndCPxZM18vLK+4Tek8YV3zOrxxP2jQeW4M9iqX13568W16dOmceqTnw1MEa6zTUugV7CCmgKo9g9WU5XHknL2+3+7ItXoFzXtX613jbX0wEKxEK1kf835q6XvMR43HnP1OCe8z0tc6cnnd7PXrYZr+Oa8D7X1rOEa13ruEaruEaruFbBy9uk3kePJLUDh+yJPJeOJJVfVPNaJTI3ZYnrxR8Gf4q13jh9biQdbB16ShNcSkuCu9I39vVcq81f2oLj03zG5v8lw3v+mJ+Wj1oov5as138r5YzV8hryX5t+heBld4JKgn7PtsnEO+fUX+SlzEX4qStCjVJuqf0o1oq13Sv5K7QeyPK7K95Uk73QSvmtZnor1JMXVMaK+GbwV7ZN90cVlcJsjCNg4mla13pfxKfpup5FV4vJ2KtQqunKC6pv7KrSf4Z4rqq3HGBGH9m+xBE7BMKQRqSpc13RSd8OfbWLEcwG08bDGAqeOyIHGMoqaJbljTxKouYrPXFEVBAey4oUyq+FyV13koRxVtaJWngT1qeGagrxbX1rOEaruEaruEaruFbDbcl1JPlY0mQX43+pHld13lsFX1P+S9sj4ivvNxH2l8u7q8NXttMWZ8maxieVuVw1b5M3XRcRTU4cfLr13wO3BxH4thyePO4sbTNIvKhtPpZ4KT9DDGBEO+Xt9jrwBPs3BE+xx0+6AUA13UEPKcdzFeOqnlZI74MG5DweC6HmgV6513 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[A Library of Functions with Transformations DemoTitle]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp Typeset`show$$ = 13 True Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`fcn$$] ^2amp original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential 13 Hold[$CellContext`a$$] 1 vertical stretch -4 4 001 13 Hold[$CellContext`b$$] 0 vertical shift -5 5 001 13 Hold[$CellContext`c$$] 0 horizontal shift -5 5 001 13 Typeset`size$$ = 400 197 203 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = 13 True $CellContext`fcn$253403$$ = False $CellContext`a$253404$$ = 13 0 $CellContext`b$253405$$ = 0 $CellContext`c$253406$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 0 $CellContext`c$$ = 0 $CellContext`fcn$$ = ^2amp 13 ControllerVariables gt 13 Hold[$CellContext`fcn$$ $CellContext`fcn$253403$$ False] 13 Hold[$CellContext`a$$ $CellContext`a$253404$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$253405$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$253406$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ 13 Body gt (If[$CellContext`a$$ == 0 $CellContext`a$$ = 0001] 13 Plot[$CellContext`b$$ + $CellContext`a$$ 13$CellContext`fcn$$[$CellContext`x - $CellContext`c$$] $CellContext`x -6 13 6 PlotRange -gt -6 6 BaseStyle -gt Medium Label 13 AxesLabel -gt $CellContext`x $CellContext`y PlotStyle -gt 13 Thickness[0005] 13 Hue[06] ImageSize -gt 400 400 AspectRatio -gt Automatic 13 Ticks -gt 13 Range[-6 6] 13 Range[-6 6] GridLines -gt 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1] 13 Table[$CellContext`n 13 RGBColor[0 06 1] $CellContext`n -6 6 1]]) 13 Specifications gt $CellContext`fcn$$ ^2amp 13 original function 13 Identity -gt linear Abs -gt absolute value (^2amp ) -gt 13 quadratic (^3amp ) -gt cubic (^(12)amp ) -gt 13 square root (Sign[] Abs[]^(13)amp ) -gt cube root Log -gt 13 logarithmic Exp -gt exponential ControlType -gt 13 SetterBar $CellContext`a$$ 1 vertical stretch -4 4 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`b$$ 0 vertical shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny $CellContext`c$$ 0 horizontal shift -5 5 001 13 Appearance -gt Labeled ControlPlacement -gt Left ImageSize -gt 13 Tiny Options gt 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt636 240 24513 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt168608005]1313Cell[TextData[13 This Demonstration shows the graph of 13 Cell[BoxData[13 FormBox[13 RowBox[y = 13 RowBox[b + 13 RowBox[a 13 RowBox[f ( 13 RowBox[x - c] )]]]] TraditionalForm]] 13 InlineMath]13 for eight basic functions You can manipulate the sliders for vertical 13stretches and vertical and horizontal shifts13] ManipulateCaption]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[Resize Images13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Click inside an image to reveal its orange resize framenDrag any of 13the orange resize handles to resize the image13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13 StyleBox[[NonBreakingSpace][FilledVerySmallSquare][NonBreakingSpace]13 FontColor-gtRGBColor[0928786 043122 0104662]]13 Cell[BoxData[13 TooltipBox[13 PaneSelectorBox[False-gtCell[TextData[StyleBox[Gamepad Controls13 FontFamily-gtVerdana]]] True-gtCell[TextData[StyleBox[13 Gamepad Controls13 FontFamily-gtVerdana13 FontColor-gtGrayLevel[05]]]] Dynamic[13 CurrentValue[MouseOver]]]13 Control this Demonstration with a gamepad or othernhuman interface 13device connected to your computer13 LabelStyle-gt13 FontFamily -gt Verdana FontSize -gt 10 FontColor -gt GrayLevel[035] 13 Background -gt GrayLevel[098]]]]13] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13ALibraryOfFunctionsWithTransformationsampversion=0007] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13ALibraryOfFunctionsWithTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[A Library of Functions with Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom13ALibraryOfFunctionsWithTransformations] None13 ButtonNote-gt13 httpdemonstrationswolframcomALibraryOfFunctionsWithTransformations13]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Ed Zaborowski13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Ed+Zabrowski] 13 None]13] Author13 FontColor-gtGrayLevel[06]]1313Cell[TextData[13 Based on a program by 13 ButtonBox[Abby Brown13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Abby+Brown] 13 None]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt374832065]1313Cell[TextData[13 [Copyright] 13 StyleBox[ButtonBox[The Wolfram Demonstrations Project amp Contributors13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 FontColor-gtGrayLevel[06]]13 [ThickSpace][ThickSpace][ThickSpace]|[ThickSpace][ThickSpace]13[ThickSpace]13 StyleBox[ButtonBox[Terms of Use13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomtermsofusehtml] None13 ButtonNote-gthttpdemonstrationswolframcomtermsofusehtml]13 FontColor-gtGrayLevel[06]]13] Text13 CellFrame-gt0 0 0 0513 CellMargins-gt48 48 20 5013 CellFrameColor-gtGrayLevel[045098]13 FontFamily-gtVerdana13 FontSize-gt913 FontColor-gtGrayLevel[06]13 CellTags-gtCopyright]1313Editable-gtFalse13Saveable-gtFalse13ScreenStyleEnvironment-gtWorking13CellGrouping-gtManual13WindowSize-gt750 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtA Library of Functions with Transformations13DockedCells-gt13CellContext-gtNotebook13FrontEndVersion-gt60 for Microsoft Windows (32-bit) (February 7 2008)13StyleDefinitions-gtNotebook[13 Cell[13 CellGroupData[13 Cell[13 Demonstration Styles Title 13 CellChangeTimes -gt 13 33509184553711^9 336928902713192^9 336928902738193^9 13 33754479092466917`^9 33754479095123196`^9 13 3375558447161495^9 3375558447395873^9 337572892702972^9 13 3375728927639103^9] 13 Cell[13 StyleData[StyleDefinitions -gt Defaultnb]] 13 Cell[13 CellGroupData[13 Cell[13 Style Environment Names Section 13 CellChangeTimes -gt 3369277974278112^9 3369277974396138^9] 13 13 Cell[13 StyleData[All Working] ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Notebook Options Section 13 CellChangeTimes -gt 3374865264950812^9 3374865265419568^9] 13 13 Cell[13 The options defined for the style below will be used at the 13Notebook level Text] 13 Cell[13 StyleData[Notebook] Editable -gt True 13 PageHeaders -gt None None None None None None 13 PageFooters -gt None None None None None None 13 PageHeaderLines -gt False False 13 PageFooterLines -gt False False 13 PrintingOptions -gt 13 FacingPages -gt False FirstPageFooter -gt False 13 RestPagesFooter -gt False CreateCellID -gt True 13 CellFrameLabelMargins -gt 6 DefaultNewInlineCellStyle -gt 13 InlineMath DefaultInlineFormatType -gt 13 DefaultTextInlineFormatType TrackCellChangeTimes -gt False 13 ShowStringCharacters -gt True CacheGraphics -gt False 13 StyleMenuListing -gt None] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 InputOutput Section 13 CellChangeTimes -gt 33756313297791014`^9 13 33756313299509783`^9] 13 Cell[13 The cells in this section define styles used for input and output 13to the kernel Be careful when modifying renaming or removing these 13styles because the front end associates special meanings with these style 13names Text] 13 Cell[13 StyleData[Input] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[Output] CellMargins -gt 48 4 6 4] 13 Cell[13 StyleData[DemonstrationHeader] Deletable -gt False 13 CellFrame -gt 0 0 0 1 ShowCellBracket -gt False 13 CellMargins -gt 0 0 30 0 13 CellGroupingRules -gt SectionGrouping 20 13 CellHorizontalScrolling -gt True 13 CellFrameMargins -gt 0 0 0 0 CellFrameColor -gt 13 RGBColor[06449835965514611 0758632791638056 02516823071641108]13 StyleMenuListing -gt None Background -gt 13 RGBColor[13 06449835965514611 0758632791638056 02516823071641108]] 13 Cell[13 StyleData[ShowSource] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None 13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold 13 FontSlant -gt Plain FontColor -gt RGBColor[1 042 0]] Closed]]13 13 Cell[13 CellGroupData[13 Cell[13 Basic Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 335686681885432^9 335686681945788^9 13 3375657418186455^9 3375657418452083^9] 13 Cell[13 StyleData[Hyperlink] StyleMenuListing -gt None FontColor -gt 13 GrayLevel[0]] 13 Cell[13 StyleData[SiteLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 GrayLevel[045098] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFrame -gt None 13 ButtonFunction gt (FrontEndExecute[13 NotebookLocate[2]]amp ) ButtonNote -gt ButtonData] 13 Cell[13 StyleData[Link] FontColor -gt GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoNotes] CellFrame -gt True 13 CellMargins -gt 0 0 0 0 ReturnCreatesNewCell -gt True 13 CellFrameMargins -gt 48 48 4 4 CellFrameColor -gt 13 GrayLevel[099] StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 10 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[DemoNotes Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[SnapshotsSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False ShowGroupOpener -gt True 13 CellMargins -gt 48 48 10 30 13 PrivateCellOptions -gt DefaultCellGroupOpen -gt False 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 SnapshotCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 SnapshotCaption StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SnapshotOutput] ShowCellBracket -gt False 13 CellMargins -gt 48 10 5 7 Evaluatable -gt True 13 CellGroupingRules -gt InputGrouping StripStyleOnPaste -gt True 13 PageBreakWithin -gt False GroupPageBreakWithin -gt False 13 DefaultFormatType -gt DefaultInputFormatType ShowAutoStyles -gt 13 True TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] 13 AutoItalicWords -gt LanguageCategory -gt Mathematica 13 FormatType -gt InputForm NumberMarks -gt True 13 LinebreakAdjustments -gt 085 2 10 0 1 CounterIncrements -gt 13 Input MenuPosition -gt 1500 MenuCommandKey -gt 9] 13 Cell[13 StyleData[SnapshotOuput Printout] 13 CellMargins -gt 39 0 4 6 13 LinebreakAdjustments -gt 085 2 10 1 1] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoTitle] Deletable -gt False ShowCellBracket -gt 13 False CellMargins -gt 48 48 22 10 13 CellGroupingRules -gt SectionGrouping 20 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 20 FontWeight -gt 13 Bold Background -gt GrayLevel[1]] 13 Cell[13 StyleData[DemoName Printout] 13 CellMargins -gt 24 8 8 27 13 HyphenationOptions -gt HyphenationCharacter -gt - FontSize -gt 13 16] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DetailsSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 25 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[0691905 0790311 0300252] StyleMenuListing -gt None13 FontFamily -gt Helvetica FontSize -gt 10 FontWeight -gt Bold13 FontColor -gt RGBColor[0691905 0790311 0300252]] 13 Cell[13 StyleData[DetailsSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoSection] CellFrame -gt 0 0 0 1 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 28 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 48 48 6 8 CellFrameColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`] 13 StyleMenuListing -gt None FontFamily -gt Helvetica FontSize -gt 13 10 FontWeight -gt Bold FontSlant -gt Plain FontColor -gt 13 RGBColor[13 06950942244602121 07903257801174944 029706263828488594`]] 13 13 Cell[13 StyleData[DemoSection Printout] 13 CellMargins -gt 12 0 0 16 PageBreakBelow -gt False 13 FontSize -gt 12] Closed]] 13 Cell[13 StyleData[ManipulateSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12] 13 Cell[13 StyleData[ManipulateCaptionSection] 13 CellFrame -gt 0 0 0 2 ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] DefaultNewCellStyle -gt 13 ManipulateCaption StyleMenuListing -gt None FontFamily -gt 13 Verdana FontSize -gt 12 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[ManipulateCaption] ShowCellBracket -gt False 13 CellMargins -gt 48 48 10 16 ReturnCreatesNewCell -gt True 13 StyleMenuListing -gt None FontFamily -gt Verdana FontSize -gt 11 13 FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 SeeAlsoSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt SeeAlso] 13 Cell[13 StyleData[SeeAlso StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 RelatedLinksSection StyleDefinitions -gt 13 StyleData[DemoSection]] ShowCellBracket -gt False 13 DefaultNewCellStyle -gt RelatedLinks] 13 Cell[13 StyleData[13 RelatedLinks StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt 13 RGBColor[0928786 043122 0104662]] ShowCellBracket -gt False 13 FontColor -gt GrayLevel[045098]] 13 Cell[13 StyleData[13 CategoriesSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Categories StyleDefinitions -gt StyleData[DemoNotes]]13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 AuthorSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 4 18 13 CellElementSpacings -gt CellMinHeight -gt 3 13 CellFrameMargins -gt 48 48 6 3 DefaultNewCellStyle -gt 13 Author FontSize -gt 1 FontColor -gt GrayLevel[1]] 13 Cell[13 StyleData[Author StyleDefinitions -gt StyleData[DemoNotes]] 13 CellDingbat -gt 13 Cell[[FilledSmallSquare] FontColor -gt GrayLevel[064]] 13 ShowCellBracket -gt False] 13 Cell[13 StyleData[13 DetailNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False FontColor -gt GrayLevel[0]] 13 Cell[13 StyleData[13 CitationSection StyleDefinitions -gt StyleData[DemoSection]] 13 ShowCellBracket -gt False CellMargins -gt 48 48 8 14 13 DefaultNewCellStyle -gt Categories] 13 Cell[13 StyleData[Citations StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False ParagraphSpacing -gt 0 6] 13 Cell[13 StyleData[13 RevisionSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt RevisionNotes] 13 Cell[13 StyleData[13 RevisionNotes StyleDefinitions -gt StyleData[DemoNotes]] 13 ShowCellBracket -gt False] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 Specific Styles Section 13 CellChangeTimes -gt 334971724802035^9 334971724966638^9 13 335091840608065^9 335091840781999^9 335091845122987^9 13 335091845356607^9 336230868322317^9 336230868335672^9 13 336928857618576^9 336928857640452^9 33737586217185173`^913 3373758622077897^9] 13 Cell[13 StyleData[InitializationSection] CellFrame -gt 0 0 0 2 13 ShowCellBracket -gt False CellMargins -gt 48 48 10 30 13 CellGroupingRules -gt SectionGrouping 30 13 CellFrameMargins -gt 8 8 8 2 CellFrameColor -gt 13 RGBColor[0870588 0521569 0121569] StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 12 FontColor -gt 13 GrayLevel[045098]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorBar] ShowCellBracket -gt False 13 CellMargins -gt 48 44 3 6 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 9 FontColor -gt 13 GrayLevel[05]] 13 Cell[13 StyleData[AnchorBar Presentation] FontSize -gt 18] 13 Cell[13 StyleData[AnchorBar SlideShow] StyleMenuListing -gt None] 13 Cell[13 StyleData[AnchorBar Printout] FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[AnchorLink] StyleMenuListing -gt None 13 ButtonStyleMenuListing -gt Automatic FontColor -gt 13 RGBColor[05 05 05] 13 ButtonBoxOptions -gt 13 Active -gt True ButtonFunction gt (FrontEndExecute[13 FrontEnd`NotebookLocate[2]]amp ) ButtonNote -gt 13 ButtonData] 13 Cell[13 StyleData[AnchorLink Printout] 13 FontVariations -gt Underline -gt False FontColor -gt 13 GrayLevel[0]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[GamePadStatus] ShowCellBracket -gt False 13 CellMargins -gt 48 48 5 5 StyleMenuListing -gt None 13 FontFamily -gt Verdana FontSize -gt 10] 13 Cell[13 StyleData[GamePadStatus Printout] 13 CellMargins -gt 24 0 0 10 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[DemoInstruction] CellMargins -gt 48 48 5 5 13 ReturnCreatesNewCell -gt True CellFrameLabelMargins -gt 2 13 MenuPosition -gt 800 MenuCommandKey -gt 8 StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 11 Background -gt 13 RGBColor[1 085 05]] 13 Cell[13 StyleData[DemoInstruction Printout] 13 CellMargins -gt 24 0 0 10 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2 FontSize -gt 9] Closed]] 13 Cell[13 StyleData[13 ImplementationSection StyleDefinitions -gt 13 StyleData[DemoSection]] Deletable -gt True DefaultNewCellStyle -gt 13 ImplementationNotes] 13 Cell[13 StyleData[13 ImplementationNotes StyleDefinitions -gt StyleData[DemoNotes]]]13 13 Cell[13 StyleData[13 StatusSection StyleDefinitions -gt StyleData[DemoSection]] 13 DefaultNewCellStyle -gt StatusNotes] 13 Cell[13 StyleData[13 StatusNotes StyleDefinitions -gt StyleData[DemoNotes]]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[SectionGloss] StyleMenuListing -gt None FontSize -gt 13 085 Inherited FontWeight -gt Plain FontColor -gt 13 GrayLevel[06]] 13 Cell[13 StyleData[SectionGloss Printout]] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineFormula] 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 Formula AutoSpacing -gt True ScriptLevel -gt 1 13 AutoMultiplicationSymbol -gt False SingleLetterItalics -gt False 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 105 Inherited 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 FractionBoxOptions -gt BaseStyle -gt SpanMaxSize -gt Automatic 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineFormula Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineOutput] CellHorizontalScrolling -gt True 13 TwoByteSyntaxCharacterAutoReplacement -gt True 13 HyphenationOptions -gt 13 HyphenationCharacter -gt [Continuation] LanguageCategory -gt 13 None AutoMultiplicationSymbol -gt False StyleMenuListing -gt 13 None FontFamily -gt Courier FontSize -gt 105 Inherited] 13 Cell[13 StyleData[InlineOutput Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[InlineMath] DefaultFormatType -gt 13 DefaultTextFormatType DefaultInlineFormatType -gt 13 TraditionalForm LanguageCategory -gt Formula AutoSpacing -gt 13 True ScriptLevel -gt 1 AutoMultiplicationSymbol -gt False 13 SingleLetterItalics -gt True SpanMaxSize -gt DirectedInfinity[1] 13 StyleMenuListing -gt None FontFamily -gt Times FontSize -gt 13 105 Inherited ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxItemSize -gt 13 Columns -gt Automatic ColumnsIndexed -gt 13 Rows -gt 1 RowsIndexed -gt ] 13 Cell[13 StyleData[InlineMath Printout] 13 CellMargins -gt 2 0 0 8] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableBase] CellMargins -gt 48 48 4 4 13 SpanMaxSize -gt 1 StyleMenuListing -gt None FontFamily -gt 13 Courier FontSize -gt 11 13 ButtonBoxOptions -gt ButtonFrame -gt None 13 GridBoxOptions -gt 13 GridBoxAlignment -gt 13 Columns -gt Left ColumnsIndexed -gt 13 Rows -gt Baseline RowsIndexed -gt ] 13 Cell[13 StyleData[TableBase Printout] 13 CellMargins -gt 2 0 0 8 FontSize -gt 9] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 1ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0966] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[0126] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 1ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0078] 13 Scaled[0922] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 2ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[005] 13 Scaled[041] 13 Scaled[0565] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 2ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[0079] 13 Scaled[0363] 13 Scaled[0558] ColumnsIndexed -gt Rows -gt 113 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[13 3ColumnTableMod StyleDefinitions -gt StyleData[TableBase]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[004] 13 Scaled[0266] 13 Scaled[026] 13 Scaled[044] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[014] 13 Offset[077] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[04] 13 Offset[02] RowsIndexed -gt ] 13 Cell[13 StyleData[13 3ColumnTableMod Printout StyleDefinitions -gt 13 StyleData[TableBase Printout]] 13 GridBoxOptions -gt GridBoxItemSize -gt Columns -gt 13 Scaled[008] 13 Scaled[025] 13 Scaled[025] 13 Scaled[042] ColumnsIndexed -gt Rows -gt 1 13 RowsIndexed -gt GridBoxSpacings -gt Columns -gt 13 Offset[028] 13 Offset[056] 13 Offset[028] ColumnsIndexed -gt Rows -gt 13 Offset[02] 13 Offset[056] 13 Offset[02] RowsIndexed -gt ] Closed]] 13 Cell[13 CellGroupData[13 Cell[13 StyleData[TableText] Deletable -gt False StyleMenuListing -gt 13 None FontFamily -gt Verdana FontSize -gt 0952 Inherited] 13 Cell[13 StyleData[TableText Printout] 13 CellMargins -gt 24 0 0 8 Hyphenation -gt True 13 HyphenationOptions -gt HyphenationCharacter -gt - 13 LineSpacing -gt 1 2 2] Closed]] 13 Cell[13 StyleData[Continuation] FontColor -gt GrayLevel[1]] Closed]] 13 Open]] Visible -gt False FrontEndVersion -gt 13 60 for Microsoft Windows (32-bit) (February 7 2008) StyleDefinitions -gt 13 Defaultnb]13]13( End of Notebook Content )1313( Internal cache information )13(CellTagsOutline13CellTagsIndex-gt13 ControlSuggestions-gt13 Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 59745 119913 Copyright 59940 120413 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 64 0 70 DemoTitle]13Cell[24978 426 3891 72 70 Output13 CellID-gt168608005]13Cell[28872 500 409 12 70 ManipulateCaption]13Cell[29284 514 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[29485 521 1373 32 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[30861 555 506 11 70 ShowSource]13Cell[31370 568 50 0 70 CitationSection]13Cell[31423 570 914 27 70 Citations]13Cell[32340 599 26 0 70 AuthorSection]13Cell[32369 601 238 8 70 Author]13Cell[32610 611 260 9 70 Author13 CellID-gt374832065]13Cell[32873 622 822 23 70 Text13 CellTags-gtCopyright]1313]13)1313( End of internal cache information )13( NotebookSignature JRELQHWvj8BFwAF7QlMs1gw )13

40Oct 29shy350 PM

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