Lesson 5 Trig functions 2013 (1)notebook

1

October 29 2013

Ene 10shy0953 am

Trigonometric Functions Revisited

bull Recognise the graphs of sine cosine and tangent functions their periods and amplitudes

bull Revise the geometrical transformations of trigonometric functions

bull Draw sketches of the trigonometric functions

Lesson 5 Trig functions 2013 (1)notebook

2

October 29 2013

Ene 10shy0953 am

Sine amp cosine from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

3

October 29 2013

Ene 10shy0953 am

Sine functionsin xx

0

π

π2

π6π3

2π3

5π6

3π22π

Lesson 5 Trig functions 2013 (1)notebook

4

October 29 2013

Ene 10shy0953 am

maximum value = 1minimum value = -1

range= [-11]

period= 2π ( or 360o)

amplitude= 1

amplitude

periodSine function

Lesson 5 Trig functions 2013 (1)notebook

5

October 29 2013

Ene 10shy0953 am

Cosine functioncos xx

0

π

π2

π6π3

2π3

5π6

3π22π Sine amp cosine from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

6

October 29 2013

Ene 10shy0953 am

maximum value = 1minimum value = -1

range= [-11]amplitude= 1

period= 2π ( or 360o)

amplitude

periodCosine function

Lesson 5 Trig functions 2013 (1)notebook

7

October 29 2013

Ene 10shy0953 am

Tangent function

httpwwwanalyzemathcomunitcircleunitcirclehtmlhttpwwwiescojpmathproductstrigappletsgraphTanXgraphTanXhtml

FromCircleToSineAndCosineCurvesWithAngleInDegreesnbp

Tan from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

2

October 29 2013

Ene 10shy0953 am

Sine amp cosine from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

3

October 29 2013

Ene 10shy0953 am

Sine functionsin xx

0

π

π2

π6π3

2π3

5π6

3π22π

Lesson 5 Trig functions 2013 (1)notebook

4

October 29 2013

Ene 10shy0953 am

maximum value = 1minimum value = -1

range= [-11]

period= 2π ( or 360o)

amplitude= 1

amplitude

periodSine function

Lesson 5 Trig functions 2013 (1)notebook

5

October 29 2013

Ene 10shy0953 am

Cosine functioncos xx

0

π

π2

π6π3

2π3

5π6

3π22π Sine amp cosine from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

6

October 29 2013

Ene 10shy0953 am

maximum value = 1minimum value = -1

range= [-11]amplitude= 1

period= 2π ( or 360o)

amplitude

periodCosine function

Lesson 5 Trig functions 2013 (1)notebook

7

October 29 2013

Ene 10shy0953 am

Tangent function

httpwwwanalyzemathcomunitcircleunitcirclehtmlhttpwwwiescojpmathproductstrigappletsgraphTanXgraphTanXhtml

FromCircleToSineAndCosineCurvesWithAngleInDegreesnbp

Tan from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

3

October 29 2013

Ene 10shy0953 am

Sine functionsin xx

0

π

π2

π6π3

2π3

5π6

3π22π

Lesson 5 Trig functions 2013 (1)notebook

4

October 29 2013

Ene 10shy0953 am

maximum value = 1minimum value = -1

range= [-11]

period= 2π ( or 360o)

amplitude= 1

amplitude

periodSine function

Lesson 5 Trig functions 2013 (1)notebook

5

October 29 2013

Ene 10shy0953 am

Cosine functioncos xx

0

π

π2

π6π3

2π3

5π6

3π22π Sine amp cosine from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

6

October 29 2013

Ene 10shy0953 am

maximum value = 1minimum value = -1

range= [-11]amplitude= 1

period= 2π ( or 360o)

amplitude

periodCosine function

Lesson 5 Trig functions 2013 (1)notebook

7

October 29 2013

Ene 10shy0953 am

Tangent function

httpwwwanalyzemathcomunitcircleunitcirclehtmlhttpwwwiescojpmathproductstrigappletsgraphTanXgraphTanXhtml

FromCircleToSineAndCosineCurvesWithAngleInDegreesnbp

Tan from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

4

October 29 2013

Ene 10shy0953 am

maximum value = 1minimum value = -1

range= [-11]

period= 2π ( or 360o)

amplitude= 1

amplitude

periodSine function

Lesson 5 Trig functions 2013 (1)notebook

5

October 29 2013

Ene 10shy0953 am

Cosine functioncos xx

0

π

π2

π6π3

2π3

5π6

3π22π Sine amp cosine from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

6

October 29 2013

Ene 10shy0953 am

maximum value = 1minimum value = -1

range= [-11]amplitude= 1

period= 2π ( or 360o)

amplitude

periodCosine function

Lesson 5 Trig functions 2013 (1)notebook

7

October 29 2013

Ene 10shy0953 am

Tangent function

httpwwwanalyzemathcomunitcircleunitcirclehtmlhttpwwwiescojpmathproductstrigappletsgraphTanXgraphTanXhtml

FromCircleToSineAndCosineCurvesWithAngleInDegreesnbp

Tan from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

5

October 29 2013

Ene 10shy0953 am

Cosine functioncos xx

0

π

π2

π6π3

2π3

5π6

3π22π Sine amp cosine from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

6

October 29 2013

Ene 10shy0953 am

maximum value = 1minimum value = -1

range= [-11]amplitude= 1

period= 2π ( or 360o)

amplitude

periodCosine function

Lesson 5 Trig functions 2013 (1)notebook

7

October 29 2013

Ene 10shy0953 am

Tangent function

httpwwwanalyzemathcomunitcircleunitcirclehtmlhttpwwwiescojpmathproductstrigappletsgraphTanXgraphTanXhtml

FromCircleToSineAndCosineCurvesWithAngleInDegreesnbp

Tan from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

6

October 29 2013

Ene 10shy0953 am

maximum value = 1minimum value = -1

range= [-11]amplitude= 1

period= 2π ( or 360o)

amplitude

periodCosine function

Lesson 5 Trig functions 2013 (1)notebook

7

October 29 2013

Ene 10shy0953 am

Tangent function

httpwwwanalyzemathcomunitcircleunitcirclehtmlhttpwwwiescojpmathproductstrigappletsgraphTanXgraphTanXhtml

FromCircleToSineAndCosineCurvesWithAngleInDegreesnbp

Tan from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

7

October 29 2013

Ene 10shy0953 am

Tangent function

httpwwwanalyzemathcomunitcircleunitcirclehtmlhttpwwwiescojpmathproductstrigappletsgraphTanXgraphTanXhtml

FromCircleToSineAndCosineCurvesWithAngleInDegreesnbp

Tan from unit circle by EVggb

Lesson 5 Trig functions 2013 (1)notebook

8

October 29 2013

Ene 10shy0953 am

period

vertical asymptotes x = π2 x = 3π2 x = 5π2

period π no amplitude

Tangent function

Lesson 5 Trig functions 2013 (1)notebook

9

October 29 2013

Ene 10shy0953 am

Transformations of the trigonometric functions

y = sin x + 2

y =2 sin x y = sin (2x)

y = shy sin x

y = sin (shyx)

in [shy2π 2π]

y = sin (x + 2)

Lesson 5 Trig functions 2013 (1)notebook

10

October 29 2013

Ene 10shy0953 am

Vertical translations

y = sin x

y = sin x +2

y = sin x shy1

y = sin x + cy = cos x + cy = tan x + c

represent vertical translations of vector

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

11

October 29 2013

Ene 10shy0953 am

y = sin x

y = cos x

period and amplitude dont change

Horizontal translations

Lesson 5 Trig functions 2013 (1)notebook

12

October 29 2013

Ene 10shy0953 am

y = sin ( x plusmna )

Horizontal translations

y = cos ( x plusmna )y = tan ( x plusmna )

represent horizontal translations of the curves y = sinx y = cos x and y = tan x

y = sin ( x + a )

y = sin ( x - a ) to the right

to the left

Lesson 5 Trig functions 2013 (1)notebook

13

October 29 2013

Ene 10shy0953 am

y = a sin xy = a cos xy = a tan x

are dilations of the curvesy = sin xy = cos x

y = tan x

parallel to the y-axis

y = cos x

y =2 cos x

the amplitude changes to |a|

Vertical dilation (stretch)

Lesson 5 Trig functions 2013 (1)notebook

14

October 29 2013

Ene 10shy0953 am

Horizontal dilation (stretch)

y = sin x

y = sin (2x)

period changes to half the original

horizontal stretch scale factor frac12period π

Lesson 5 Trig functions 2013 (1)notebook

15

October 29 2013

Ene 10shy0953 am

horizontal stretch scale factor 3

y = sin x

period changes to three times the original

period= 2 π

period= 6 π

Lesson 5 Trig functions 2013 (1)notebook

16

October 29 2013

Ene 10shy0953 am

y = sin (bx)

y = cos(b x)

y = tan( bx)

are dilations of the curves y = sin xy = cos x

y = tan x

parallel to the x-axis

the period changes to

is a dilation of the curve parallel to the x-axis

the period changes to

Lesson 5 Trig functions 2013 (1)notebook

17

October 29 2013

Ene 10shy0953 am

Reflections

y = sin x

y = shy sin x

y = tan x

y = tan(shyx)

reflection in the x-axis

reflection in the y-axis

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

18

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a sin [b(xshy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a| (vertical dilation)

the same applies for cosine function

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

9

October 29 2013

Ene 10shy0953 am

Transformations of the trigonometric functions

y = sin x + 2

y =2 sin x y = sin (2x)

y = shy sin x

y = sin (shyx)

in [shy2π 2π]

y = sin (x + 2)

Lesson 5 Trig functions 2013 (1)notebook

10

October 29 2013

Ene 10shy0953 am

Vertical translations

y = sin x

y = sin x +2

y = sin x shy1

y = sin x + cy = cos x + cy = tan x + c

represent vertical translations of vector

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

11

October 29 2013

Ene 10shy0953 am

y = sin x

y = cos x

period and amplitude dont change

Horizontal translations

Lesson 5 Trig functions 2013 (1)notebook

12

October 29 2013

Ene 10shy0953 am

y = sin ( x plusmna )

Horizontal translations

y = cos ( x plusmna )y = tan ( x plusmna )

represent horizontal translations of the curves y = sinx y = cos x and y = tan x

y = sin ( x + a )

y = sin ( x - a ) to the right

to the left

Lesson 5 Trig functions 2013 (1)notebook

13

October 29 2013

Ene 10shy0953 am

y = a sin xy = a cos xy = a tan x

are dilations of the curvesy = sin xy = cos x

y = tan x

parallel to the y-axis

y = cos x

y =2 cos x

the amplitude changes to |a|

Vertical dilation (stretch)

Lesson 5 Trig functions 2013 (1)notebook

14

October 29 2013

Ene 10shy0953 am

Horizontal dilation (stretch)

y = sin x

y = sin (2x)

period changes to half the original

horizontal stretch scale factor frac12period π

Lesson 5 Trig functions 2013 (1)notebook

15

October 29 2013

Ene 10shy0953 am

horizontal stretch scale factor 3

y = sin x

period changes to three times the original

period= 2 π

period= 6 π

Lesson 5 Trig functions 2013 (1)notebook

16

October 29 2013

Ene 10shy0953 am

y = sin (bx)

y = cos(b x)

y = tan( bx)

are dilations of the curves y = sin xy = cos x

y = tan x

parallel to the x-axis

the period changes to

is a dilation of the curve parallel to the x-axis

the period changes to

Lesson 5 Trig functions 2013 (1)notebook

17

October 29 2013

Ene 10shy0953 am

Reflections

y = sin x

y = shy sin x

y = tan x

y = tan(shyx)

reflection in the x-axis

reflection in the y-axis

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

18

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a sin [b(xshy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a| (vertical dilation)

the same applies for cosine function

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

10

October 29 2013

Ene 10shy0953 am

Vertical translations

y = sin x

y = sin x +2

y = sin x shy1

y = sin x + cy = cos x + cy = tan x + c

represent vertical translations of vector

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

11

October 29 2013

Ene 10shy0953 am

y = sin x

y = cos x

period and amplitude dont change

Horizontal translations

Lesson 5 Trig functions 2013 (1)notebook

12

October 29 2013

Ene 10shy0953 am

y = sin ( x plusmna )

Horizontal translations

y = cos ( x plusmna )y = tan ( x plusmna )

represent horizontal translations of the curves y = sinx y = cos x and y = tan x

y = sin ( x + a )

y = sin ( x - a ) to the right

to the left

Lesson 5 Trig functions 2013 (1)notebook

13

October 29 2013

Ene 10shy0953 am

y = a sin xy = a cos xy = a tan x

are dilations of the curvesy = sin xy = cos x

y = tan x

parallel to the y-axis

y = cos x

y =2 cos x

the amplitude changes to |a|

Vertical dilation (stretch)

Lesson 5 Trig functions 2013 (1)notebook

14

October 29 2013

Ene 10shy0953 am

Horizontal dilation (stretch)

y = sin x

y = sin (2x)

period changes to half the original

horizontal stretch scale factor frac12period π

Lesson 5 Trig functions 2013 (1)notebook

15

October 29 2013

Ene 10shy0953 am

horizontal stretch scale factor 3

y = sin x

period changes to three times the original

period= 2 π

period= 6 π

Lesson 5 Trig functions 2013 (1)notebook

16

October 29 2013

Ene 10shy0953 am

y = sin (bx)

y = cos(b x)

y = tan( bx)

are dilations of the curves y = sin xy = cos x

y = tan x

parallel to the x-axis

the period changes to

is a dilation of the curve parallel to the x-axis

the period changes to

Lesson 5 Trig functions 2013 (1)notebook

17

October 29 2013

Ene 10shy0953 am

Reflections

y = sin x

y = shy sin x

y = tan x

y = tan(shyx)

reflection in the x-axis

reflection in the y-axis

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

18

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a sin [b(xshy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a| (vertical dilation)

the same applies for cosine function

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

11

October 29 2013

Ene 10shy0953 am

y = sin x

y = cos x

period and amplitude dont change

Horizontal translations

Lesson 5 Trig functions 2013 (1)notebook

12

October 29 2013

Ene 10shy0953 am

y = sin ( x plusmna )

Horizontal translations

y = cos ( x plusmna )y = tan ( x plusmna )

represent horizontal translations of the curves y = sinx y = cos x and y = tan x

y = sin ( x + a )

y = sin ( x - a ) to the right

to the left

Lesson 5 Trig functions 2013 (1)notebook

13

October 29 2013

Ene 10shy0953 am

y = a sin xy = a cos xy = a tan x

are dilations of the curvesy = sin xy = cos x

y = tan x

parallel to the y-axis

y = cos x

y =2 cos x

the amplitude changes to |a|

Vertical dilation (stretch)

Lesson 5 Trig functions 2013 (1)notebook

14

October 29 2013

Ene 10shy0953 am

Horizontal dilation (stretch)

y = sin x

y = sin (2x)

period changes to half the original

horizontal stretch scale factor frac12period π

Lesson 5 Trig functions 2013 (1)notebook

15

October 29 2013

Ene 10shy0953 am

horizontal stretch scale factor 3

y = sin x

period changes to three times the original

period= 2 π

period= 6 π

Lesson 5 Trig functions 2013 (1)notebook

16

October 29 2013

Ene 10shy0953 am

y = sin (bx)

y = cos(b x)

y = tan( bx)

are dilations of the curves y = sin xy = cos x

y = tan x

parallel to the x-axis

the period changes to

is a dilation of the curve parallel to the x-axis

the period changes to

Lesson 5 Trig functions 2013 (1)notebook

17

October 29 2013

Ene 10shy0953 am

Reflections

y = sin x

y = shy sin x

y = tan x

y = tan(shyx)

reflection in the x-axis

reflection in the y-axis

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

18

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a sin [b(xshy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a| (vertical dilation)

the same applies for cosine function

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

12

October 29 2013

Ene 10shy0953 am

y = sin ( x plusmna )

Horizontal translations

y = cos ( x plusmna )y = tan ( x plusmna )

represent horizontal translations of the curves y = sinx y = cos x and y = tan x

y = sin ( x + a )

y = sin ( x - a ) to the right

to the left

Lesson 5 Trig functions 2013 (1)notebook

13

October 29 2013

Ene 10shy0953 am

y = a sin xy = a cos xy = a tan x

are dilations of the curvesy = sin xy = cos x

y = tan x

parallel to the y-axis

y = cos x

y =2 cos x

the amplitude changes to |a|

Vertical dilation (stretch)

Lesson 5 Trig functions 2013 (1)notebook

14

October 29 2013

Ene 10shy0953 am

Horizontal dilation (stretch)

y = sin x

y = sin (2x)

period changes to half the original

horizontal stretch scale factor frac12period π

Lesson 5 Trig functions 2013 (1)notebook

15

October 29 2013

Ene 10shy0953 am

horizontal stretch scale factor 3

y = sin x

period changes to three times the original

period= 2 π

period= 6 π

Lesson 5 Trig functions 2013 (1)notebook

16

October 29 2013

Ene 10shy0953 am

y = sin (bx)

y = cos(b x)

y = tan( bx)

are dilations of the curves y = sin xy = cos x

y = tan x

parallel to the x-axis

the period changes to

is a dilation of the curve parallel to the x-axis

the period changes to

Lesson 5 Trig functions 2013 (1)notebook

17

October 29 2013

Ene 10shy0953 am

Reflections

y = sin x

y = shy sin x

y = tan x

y = tan(shyx)

reflection in the x-axis

reflection in the y-axis

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

18

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a sin [b(xshy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a| (vertical dilation)

the same applies for cosine function

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

13

October 29 2013

Ene 10shy0953 am

y = a sin xy = a cos xy = a tan x

are dilations of the curvesy = sin xy = cos x

y = tan x

parallel to the y-axis

y = cos x

y =2 cos x

the amplitude changes to |a|

Vertical dilation (stretch)

Lesson 5 Trig functions 2013 (1)notebook

14

October 29 2013

Ene 10shy0953 am

Horizontal dilation (stretch)

y = sin x

y = sin (2x)

period changes to half the original

horizontal stretch scale factor frac12period π

Lesson 5 Trig functions 2013 (1)notebook

15

October 29 2013

Ene 10shy0953 am

horizontal stretch scale factor 3

y = sin x

period changes to three times the original

period= 2 π

period= 6 π

Lesson 5 Trig functions 2013 (1)notebook

16

October 29 2013

Ene 10shy0953 am

y = sin (bx)

y = cos(b x)

y = tan( bx)

are dilations of the curves y = sin xy = cos x

y = tan x

parallel to the x-axis

the period changes to

is a dilation of the curve parallel to the x-axis

the period changes to

Lesson 5 Trig functions 2013 (1)notebook

17

October 29 2013

Ene 10shy0953 am

Reflections

y = sin x

y = shy sin x

y = tan x

y = tan(shyx)

reflection in the x-axis

reflection in the y-axis

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

18

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a sin [b(xshy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a| (vertical dilation)

the same applies for cosine function

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

14

October 29 2013

Ene 10shy0953 am

Horizontal dilation (stretch)

y = sin x

y = sin (2x)

period changes to half the original

horizontal stretch scale factor frac12period π

Lesson 5 Trig functions 2013 (1)notebook

15

October 29 2013

Ene 10shy0953 am

horizontal stretch scale factor 3

y = sin x

period changes to three times the original

period= 2 π

period= 6 π

Lesson 5 Trig functions 2013 (1)notebook

16

October 29 2013

Ene 10shy0953 am

y = sin (bx)

y = cos(b x)

y = tan( bx)

are dilations of the curves y = sin xy = cos x

y = tan x

parallel to the x-axis

the period changes to

is a dilation of the curve parallel to the x-axis

the period changes to

Lesson 5 Trig functions 2013 (1)notebook

17

October 29 2013

Ene 10shy0953 am

Reflections

y = sin x

y = shy sin x

y = tan x

y = tan(shyx)

reflection in the x-axis

reflection in the y-axis

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

18

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a sin [b(xshy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a| (vertical dilation)

the same applies for cosine function

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

15

October 29 2013

Ene 10shy0953 am

horizontal stretch scale factor 3

y = sin x

period changes to three times the original

period= 2 π

period= 6 π

Lesson 5 Trig functions 2013 (1)notebook

16

October 29 2013

Ene 10shy0953 am

y = sin (bx)

y = cos(b x)

y = tan( bx)

are dilations of the curves y = sin xy = cos x

y = tan x

parallel to the x-axis

the period changes to

is a dilation of the curve parallel to the x-axis

the period changes to

Lesson 5 Trig functions 2013 (1)notebook

17

October 29 2013

Ene 10shy0953 am

Reflections

y = sin x

y = shy sin x

y = tan x

y = tan(shyx)

reflection in the x-axis

reflection in the y-axis

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

18

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a sin [b(xshy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a| (vertical dilation)

the same applies for cosine function

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

16

October 29 2013

Ene 10shy0953 am

y = sin (bx)

y = cos(b x)

y = tan( bx)

are dilations of the curves y = sin xy = cos x

y = tan x

parallel to the x-axis

the period changes to

is a dilation of the curve parallel to the x-axis

the period changes to

Lesson 5 Trig functions 2013 (1)notebook

17

October 29 2013

Ene 10shy0953 am

Reflections

y = sin x

y = shy sin x

y = tan x

y = tan(shyx)

reflection in the x-axis

reflection in the y-axis

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

18

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a sin [b(xshy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a| (vertical dilation)

the same applies for cosine function

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

17

October 29 2013

Ene 10shy0953 am

Reflections

y = sin x

y = shy sin x

y = tan x

y = tan(shyx)

reflection in the x-axis

reflection in the y-axis

period and amplitude dont change

Lesson 5 Trig functions 2013 (1)notebook

18

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a sin [b(xshy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a| (vertical dilation)

the same applies for cosine function

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

18

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a sin [b(xshy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a| (vertical dilation)

the same applies for cosine function

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

19

October 29 2013

Ene 10shy0953 am

Combined transformations

y= a tan [b(x shy c)]+ dvertical translation

horizontal translation

horizontal dilation period =

amplitude= |a|

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

20

October 29 2013

Ene 10shy0953 am

Transformations sineggb

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Lesson 5 Trig functions 2013 (1)notebook

21

October 29 2013

Ene 10shy0953 am

Other related websites you can visit

httpwwwiescojpmathproductstrigappletsgraphSinXgraphSinXhtml

httpmagnusshykarlssonnumathpletstrigtrigfunchtml

httpwwwmathsnetnetasa2modulesp13unitcircle3html

lthttp2072074198pubflash15graphingswfgt

httpmembersshawcaronblondscAPPLETindexhtml

Book Ex 8D 8 E

Adjuntos

functions transformationsnbp

Sine amp cosine from unit circle by EVggb

Transformations sineggb

FromCircleToSineAndCosineCurvesWithAngleInDegreesnbp

Tan from unit circle by EVggb

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 ] 0 0 1600 30 0 25513 ColorFunction-gtRGBColor]13 ImageSize-gt1600 3013 PlotRange-gt0 1600 0 30]] DemonstrationHeader]1313Cell[Function Transformations DemoTitle13 CellID-gt700863240]1313Cell[BoxData[13 TagBox[13 StyleBox[13 DynamicModuleBox[$CellContext`a$$ = 1 $CellContext`b$$ = 13 1 $CellContext`c$$ = 0 $CellContext`d$$ = 1 $CellContext`fff$$ = 13 1 $CellContext`options$$ = $CellContext`sp $CellContext`pl 13$CellContext`reset$$ = False $CellContext`xval$$ = 0 Typeset`show$$ = True 13 Typeset`bookmarkList$$ = Typeset`bookmarkMode$$ = Menu 13 Typeset`animator$$ Typeset`animvar$$ = 1 Typeset`name$$ = 13 untitled Typeset`specs$$ = 13 Hold[$CellContext`a$$] 1 -49 49 01 13 Hold[$CellContext`b$$] 1 -49 49 01 13 Hold[$CellContext`c$$] 0 -49 49 01 13 Hold[$CellContext`d$$] 1 -49 49 01 13 Hold[$CellContext`xval$$] 0 x-value -49 49 01 13 Hold[$CellContext`reset$$] False reset False True 13 Hold[$CellContext`fff$$] 1 13 1 -gt linear 2 -gt quadratic 3 -gt cubic 4 -gt sine 5 -gt 13 exponential 6 -gt piecewise 13 Hold[$CellContext`options$$] $CellContext`sp $CellContext`pl 13 $CellContext`pl -gt plot label $CellContext`sp -gt 13 point location $CellContext`grid -gt 13 grid lines $CellContext`format -gt large format 13 Typeset`size$$ = 380 205 212 Typeset`update$$ = 0 13 Typeset`initDone$$ Typeset`skipInitDone$$ = True $CellContext`a$655$$ = 13 0 $CellContext`b$656$$ = 0 $CellContext`c$657$$ = 13 0 $CellContext`d$658$$ = 0 $CellContext`xval$659$$ = 13 0 $CellContext`reset$660$$ = False $CellContext`fff$661$$ = 13 0 $CellContext`options$662$$ = 0 13 DynamicBox[Manipulate`ManipulateBoxes[13 1 StandardForm 13 Variables gt $CellContext`a$$ = 1 $CellContext`b$$ = 13 1 $CellContext`c$$ = 0 $CellContext`d$$ = 1 $CellContext`fff$$ = 13 1 $CellContext`options$$ = $CellContext`sp $CellContext`pl 13$CellContext`reset$$ = False $CellContext`xval$$ = 0 13 ControllerVariables gt 13 Hold[$CellContext`a$$ $CellContext`a$655$$ 0] 13 Hold[$CellContext`b$$ $CellContext`b$656$$ 0] 13 Hold[$CellContext`c$$ $CellContext`c$657$$ 0] 13 Hold[$CellContext`d$$ $CellContext`d$658$$ 0] 13 Hold[$CellContext`xval$$ $CellContext`xval$659$$ 0] 13 Hold[$CellContext`reset$$ $CellContext`reset$660$$ False] 13 Hold[$CellContext`fff$$ $CellContext`fff$661$$ 0] 13 Hold[$CellContext`options$$ $CellContext`options$662$$ 0] 13 OtherVariables gt 13 Typeset`show$$ Typeset`bookmarkList$$ Typeset`bookmarkMode$$ 13 Typeset`animator$$ Typeset`animvar$$ Typeset`name$$ 13 Typeset`specs$$ Typeset`size$$ Typeset`update$$ Typeset`initDone$$13 Typeset`skipInitDone$$ Body gt 13 DynamicModule[$CellContext`function $CellContext`buttonText 13$CellContext`color1 = RGBColor[1 0 0] $CellContext`color2 = 13 RGBColor[0 0 1] 13 If[$CellContext`reset$$ == 13 True $CellContext`a$$ $CellContext`b$$ $CellContext`c$$ 13$CellContext`d$$ $CellContext`xval$$ = 1 1 0 0 13 0 $CellContext`reset$$ = False] $CellContext`function[13 Pattern[$CellContext`x 13 13 Blank[]]] = $CellContext`x $CellContext`x^2 (((113 5) $CellContext`x) ($CellContext`x - 1)) ($CellContext`x + 3) 13 Sin[$CellContext`x] 13 Exp[$CellContext`x] 13 Piecewise[3 $CellContext`x lt -3 13 Abs[$CellContext`x] 13 13 Inequality[-3 LessEqual $CellContext`x Less 13 1] -($CellContext`x - 2)^2 + 4 $CellContext`x gt= 13 1] $CellContext`buttonText = 13 linear quadratic cubic sine exponential 13 piecewise $CellContext`functionButtons = 13 Map[Part[ 1] -gt Part[ 2]amp 13 Transpose[13 Range[13 Length[$CellContext`buttonText]] $CellContext`buttonText]] 13 Show[13 Graphics[13 If[13 MemberQ[$CellContext`options$$ $CellContext`sp] 13 Text[13 ToString[13 Style[13 Round[$CellContext`xval$$ 001] 13 Part[13 $CellContext`function[13 13 Round[$CellContext`xval$$ 13 001]] $CellContext`fff$$] $CellContext`color1] 13 TraditionalForm] 475 -425 1 13 0] $CellContext`color1] 13 If[13 MemberQ[$CellContext`options$$ $CellContext`sp] 13 Text[13 ToString[13 Style[13 13 If[$CellContext`b$$ == 13 0 (1$CellContext`b$$) 13 Round[$CellContext`xval$$ 13 001] + $CellContext`c$$ $CellContext`a$$ Part[13 $CellContext`function[13 13 Round[$CellContext`xval$$ 13 001]] $CellContext`fff$$] + $CellContext`d$$ 13 ] $CellContext`color2] TraditionalForm] 13 475 -475 1 0] $CellContext`color1] 13 AbsolutePointSize[9] $CellContext`color2 13 Dashing[001] 13 If[$CellContext`b$$ == 0 13 13 Point[(1$CellContext`b$$) $CellContext`xval$$ + 13$CellContext`c$$ $CellContext`a$$ Part[13 $CellContext`function[$CellContext`xval$$] 13$CellContext`fff$$] + $CellContext`d$$] $CellContext`color2] 13 If[$CellContext`b$$ == 0 13 Line[0 $CellContext`a$$ Part[13 $CellContext`function[$CellContext`xval$$] 13$CellContext`fff$$] + $CellContext`d$$ (13 1$CellContext`b$$) $CellContext`xval$$ + 13$CellContext`c$$ $CellContext`a$$ Part[13 $CellContext`function[$CellContext`xval$$] 13$CellContext`fff$$] + $CellContext`d$$] $CellContext`color2] 13 If[$CellContext`b$$ == 0 13 13 Line[(1$CellContext`b$$) $CellContext`xval$$ + 13$CellContext`c$$ 13 0 (1$CellContext`b$$) $CellContext`xval$$ + 13$CellContext`c$$ $CellContext`a$$ Part[13 $CellContext`function[$CellContext`xval$$] 13$CellContext`fff$$] + $CellContext`d$$] $CellContext`color2] 13$CellContext`color1 13 Dashing[002] 13 Point[$CellContext`xval$$ 13 Part[13 $CellContext`function[$CellContext`xval$$] 13$CellContext`fff$$]] 13 Line[0 13 Part[13 $CellContext`function[$CellContext`xval$$] 13$CellContext`fff$$] $CellContext`xval$$ 13 Part[13 $CellContext`function[$CellContext`xval$$] 13$CellContext`fff$$]] 13 Line[$CellContext`xval$$ 0 $CellContext`xval$$ 13 Part[13 $CellContext`function[$CellContext`xval$$] 13$CellContext`fff$$]]] 13 Plot[$CellContext`a$$ Part[13 $CellContext`function[$CellContext`b$$ ($CellContext`x - 13$CellContext`c$$)] $CellContext`fff$$] + $CellContext`d$$ $CellContext`x 13 13 Which[$CellContext`b$$ lt 13 0 (1$CellContext`b$$) $CellContext`xval$$ + 13$CellContext`c$$ $CellContext`b$$ == 0 -5 $CellContext`b$$ gt 0 -5] 13 13 Which[$CellContext`b$$ lt 0 5 $CellContext`b$$ == 0 13 5 $CellContext`b$$ gt 13 0 (1$CellContext`b$$) $CellContext`xval$$ + 13$CellContext`c$$] PlotStyle -gt $CellContext`color2 13 AbsoluteThickness[3] PlotRange -gt All] 13 Plot[$CellContext`a$$ Part[13 $CellContext`function[$CellContext`b$$ ($CellContext`x - 13$CellContext`c$$)] $CellContext`fff$$] + $CellContext`d$$ $CellContext`x 13 13 Which[$CellContext`b$$ lt 0 -5 $CellContext`b$$ == 13 0 -5 $CellContext`b$$ gt 13 0 (1$CellContext`b$$) $CellContext`xval$$ + 13$CellContext`c$$] 13 13 Which[$CellContext`b$$ lt 13 0 (1$CellContext`b$$) $CellContext`xval$$ + 13$CellContext`c$$ $CellContext`b$$ == 0 5 $CellContext`b$$ gt 0 5] 13 PlotStyle -gt $CellContext`color2 PlotRange -gt All] 13 Plot[13 Part[13 $CellContext`function[$CellContext`x] $CellContext`fff$$] 13$CellContext`x -5 $CellContext`xval$$ 13 PlotStyle -gt $CellContext`color1 13 AbsoluteThickness[3] PlotRange -gt All] 13 Plot[13 Part[13 $CellContext`function[$CellContext`x] $CellContext`fff$$] 13$CellContext`x $CellContext`xval$$ 5 PlotStyle -gt $CellContext`color1 13 PlotRange -gt All] PlotRange -gt -5 5 -5 5 Axes -gt True13 AxesStyle -gt AbsoluteThickness[13 If[13 MemberQ[$CellContext`options$$ $CellContext`grid] 125 1]] 13 PlotLabel -gt If[13 MemberQ[$CellContext`options$$ $CellContext`pl] 13 Grid[13 ToString[13 Style[13 HoldForm[$CellContext`f][13 HoldForm[$CellContext`x]] $CellContext`color1] 13 TraditionalForm] 13 ToString[13 Style[If[Round[$CellContext`a$$ 01] == 1 1 13 If[13 Round[$CellContext`a$$ 01] == 0 0 $CellContext`a$$]] 13 HoldForm[$CellContext`f][13 If[Round[$CellContext`b$$ 01] == 1 1 13 If[13 Round[$CellContext`b$$ 01] == 0 13 0 $CellContext`b$$]] (HoldForm[$CellContext`x] - If[13 Round[$CellContext`c$$ 01] == 0 13 0 $CellContext`c$$])] + 13 If[Round[$CellContext`d$$ 01] == 0 13 0 $CellContext`d$$] $CellContext`color2] 13 TraditionalForm]]] ImageSize -gt If[13 MemberQ[$CellContext`options$$ $CellContext`format] 500 380] 13 BaseStyle -gt FontSize -gt If[13 MemberQ[$CellContext`options$$ $CellContext`format] Large 13 Medium] GridLines -gt If[13 MemberQ[$CellContext`options$$ $CellContext`grid] 13 Range[-5 5] 13 Range[-5 5] None]]] 13 Specifications gt $CellContext`a$$ 1 -49 49 01 ImageSize -gt 13 Dynamic[13 If[13 MemberQ[$CellContext`options$$ $CellContext`format] Medium 13 Tiny]] $CellContext`b$$ 1 -49 49 01 ImageSize -gt 13 Dynamic[13 If[13 MemberQ[$CellContext`options$$ $CellContext`format] Medium 13 Tiny]] $CellContext`c$$ 0 -49 49 01 ImageSize -gt 13 Dynamic[13 If[13 MemberQ[$CellContext`options$$ $CellContext`format] Medium 13 Tiny]] $CellContext`d$$ 1 -49 49 01 ImageSize -gt 13 Dynamic[13 If[13 MemberQ[$CellContext`options$$ $CellContext`format] Medium 13 Tiny]] 13 Delimiter $CellContext`xval$$ 0 x-value -49 49 01 13 ImageSize -gt Dynamic[13 If[13 MemberQ[$CellContext`options$$ $CellContext`format] Medium 13 Tiny]] 13 Delimiter $CellContext`reset$$ False reset False True 13 Delimiter $CellContext`fff$$ 1 13 1 -gt linear 2 -gt quadratic 3 -gt cubic 4 -gt sine 5 -gt 13 exponential 6 -gt piecewise ControlType -gt RadioButtonBar 13 Appearance -gt Vertical 13 Delimiter $CellContext`options$$ $CellContext`sp 13$CellContext`pl $CellContext`pl -gt plot label $CellContext`sp -gt 13 point location $CellContext`grid -gt 13 grid lines $CellContext`format -gt large format ControlType -gt 13 CheckboxBar Appearance -gt Vertical 13 Options gt 13 ControlPlacement -gt Left 13 AutorunSequencing -gt 1 3 3 3 5 3 7 6 13 DefaultOptions gt ControllerLinking -gt True]13 ImageSizeCache-gt550 233 23813 SingleEvaluation-gtTrue]13 DeinitializationgtNone13 DynamicModuleValuesgt13 SynchronousInitialization-gtTrue13 UnsavedVariablesgtTypeset`initDone$$13 UntrackedVariablesgtTypeset`size$$] Manipulate13 Deployed-gtTrue13 StripOnInput-gtFalse]13 Manipulate`InterpretManipulate[1]]] Output13 CellID-gt57421256]1313Cell[TextData[13 This Demonstration allows you to investigate the transformation of the 13graph of a function 13 Cell[BoxData[13 FormBox[13 RowBox[f ( x )] TraditionalForm]] InlineMath]13 to 13 Cell[BoxData[13 FormBox[13 RowBox[13 RowBox[a 13 RowBox[f ( 13 RowBox[b 13 RowBox[( 13 RowBox[x - c] )]] )]] + d] 13 TraditionalForm]] InlineMath]13 for various values of the parameters 13 Cell[BoxData[13 FormBox[a TraditionalForm]] InlineMath]13 13 Cell[BoxData[13 FormBox[b TraditionalForm]] InlineMath]13 13 Cell[BoxData[13 FormBox[c TraditionalForm]] InlineMath]13 and 13 Cell[BoxData[13 FormBox[d TraditionalForm]] InlineMath]13 In addition to showing the original and transformed curves it displays 13an individual movable point on the original curve and the image of the point 13on the transformed curve The Demonstration also divides the original curve 13into two portions and shows the images of these two portions on the 13transformed curve to emphasize how negative 13 Cell[BoxData[13 FormBox[b TraditionalForm]] InlineMath]13 values can affect the transformation13] ManipulateCaption13 CellID-gt1044312921]1313Cell[THINGS TO TRY ManipulateCaption13 FontSize-gt1013 FontSlant-gtPlain13 FontColor-gtRGBColor[13 06950942244602121 07903257801174944 029706263828488594`]13 CellTags-gtControlSuggestions]1313Cell[TextData[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]]]]] ManipulateCaption13 CellMargins-gtInherited Inherited 0 013 Deployed-gtTrue13 FontFamily-gtVerdana13 CellTags-gtControlSuggestions]1313Cell[DETAILS DetailsSection]1313Cell[TextData[13 Click the + icon next to any parameter slider to enter a specific value or 13create an animation The 13 StyleBox[reset13 FontSlant-gtItalic]13 checkbox will reset the parameter values to 13 Cell[BoxData[13 FormBox[13 RowBox[a = 1] TraditionalForm]] InlineMath]13 13 Cell[BoxData[13 FormBox[13 RowBox[b = 1] TraditionalForm]] InlineMath]13 13 Cell[BoxData[13 FormBox[13 RowBox[c = 0] TraditionalForm]] InlineMath]13 13 Cell[BoxData[13 FormBox[13 RowBox[d = 0] TraditionalForm]] InlineMath]13 and 13 Cell[BoxData[13 FormBox[13 RowBox[13 RowBox[x - value] = 0] TraditionalForm]] 13 InlineMath]13 13] DetailNotes13 CellID-gt523544941]1313Cell[RELATED LINKS RelatedLinksSection]1313Cell[TextData[13 ButtonBox[Function13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpmathworldwolframcomFunctionhtml] None]13 (13 ButtonBox[Wolfram13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpmathworldwolframcom] None13 ButtonNote-gthttpmathworldwolframcom]13 13 StyleBox[ButtonBox[MathWorld13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpmathworldwolframcom] None13 ButtonNote-gthttpmathworldwolframcom]13 FontSlant-gtItalic]13 )13] RelatedLinks13 CellID-gt329405206]1313Cell[TextData[StyleBox[ButtonBox[DOWNLOAD DEMONSTRATION SOURCE CODE 13[RightGuillemet]13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomversionssourcejspid=13FunctionTransformationsampversion=0012] None13 ButtonNote-gt13 httpdemonstrationswolframcomFunctionTransformations13FunctionTransformations-sourcenb]13 FontWeight-gtBold13 FontColor-gtRGBColor[0928786 043122 0104662]]] ShowSource13 FontSize-gt10]1313Cell[PERMANENT CITATION DATA CitationSection]1313Cell[TextData[13 13 ButtonBox[Function Transformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcomFunctionTransformations] None13 ButtonNote-gthttpdemonstrationswolframcomFunctionTransformations]13 13 from 13 ButtonBox[The Wolfram Demonstrations Project13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcom] None13 ButtonNote-gthttpdemonstrationswolframcom]13 [ParagraphSeparator][NonBreakingSpace]13 ButtonBox[httpdemonstrationswolframcomFunctionTransformations13 BaseStyle-gtSiteLink13 ButtonData-gt13 URL[httpdemonstrationswolframcomFunctionTransformations] None13 ButtonNote-gthttpdemonstrationswolframcomFunctionTransformations]13] Citations]1313Cell[ AuthorSection]1313Cell[TextData[13 Contributed by 13 ButtonBox[Eric Schulz13 BaseStyle-gtHyperlink13 ButtonData-gt13 URL[httpdemonstrationswolframcomauthorhtmlauthor=Eric+Schulz] 13 None13 ButtonNote-gt13 httpdemonstrationswolframcomauthorhtmlauthor=Eric+Schulz]13] Author13 FontColor-gtGrayLevel[06]13 CellID-gt1899227437]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-gt700 65013WindowMargins-gt0 Automatic Automatic 013WindowElements-gt13 StatusArea MemoryMonitor MagnificationPopUp VerticalScrollBar 13 MenuBar13WindowTitle-gtFunction 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[13 [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[38930 729 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Cell[39131 736 689 15 70 ManipulateCaption13 CellTags-gtControlSuggestions]13 Copyright-gt13 Cell[42927 862 822 23 70 Text13 CellTags-gtCopyright]13 13)13(CellTagsIndex13CellTagsIndex-gt13 ControlSuggestions 69792 144013 Copyright 69986 144513 13)13(NotebookFileOutline13Notebook[13Cell[568 21 24340 401 70 DemonstrationHeader]13Cell[24911 424 65 1 70 DemoTitle13 CellID-gt700863240]13Cell[24979 427 12670 261 70 Output13 CellID-gt57421256]13Cell[37652 690 1275 37 70 ManipulateCaption13 CellID-gt1044312921]13Cell[38930 729 198 5 70 ManipulateCaption13 CellTags-gtControlSuggestions]13Cell[39131 736 689 15 70 ManipulateCaption13 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