3.4 Notes.notebook 8th feb 2013

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February 08, 2013

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3.4 Combining Transformations of Functions

Use the marked points to decide whether a translation (shift)or a stretch/compression has happened in each case.

1) 2)

1) ________________________

2) ________________________

3.4 Notes.notebook 8th feb 2013

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Orally, if we start with the absolute value graph of x,how would each of these transformations affect that graph??

3.4 Notes.notebook 8th feb 2013

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f(x)

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When we factor all of our transformations we arrive at thefollowing total:

y=f(x) can be changed into:

y=a f(b(x­h))+k where:

a is the vertical stretch/compressionb is the horizontal stretch compressionh is the horizontal shift (translation)k is the vertical shift (translation)

YOU MUST UNDERSTAND ALL OF THESE AND NOT CONFUSE THEM!!

3.4 Notes.notebook 8th feb 2013

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Ex) If point (8,­4) is on f(x) then what point is on 2f(2(x­2))+2.

The point would be ( (8/2+2) , (­4*2+2)) =(6,­6)

Tip: Work left to rightFind the x value first by looking at the b and h transformationsThen find the y value by looking at the a and k transformations

3.4 Notes.notebook 8th feb 2013

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February 08, 2013

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If (8,­4) is on f(x) then what point must be on the following:

a) 3f(4(x+1)) __________

b) 2f(1/2x)+3 __________

c) ­4f(x+2)+6 __________

d) ­f(­2(x­1))­2 _________

e) f(2x­4) ___________ This is a trick question!! Beware oh "h"

f) 4f(3x+6) ­ 1 __________

3.4 Notes.notebook 8th feb 2013

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3.4 Notes.notebook 8th feb 2013

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Notice that the asymptotealso has to shift!

3.4 Notes.notebook 8th feb 2013

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February 08, 2013

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We can plot the changes to the key pointsusing this chart

OR

We can think of the transformation as;y=2f(­1(x­3))­1 and replot the points.This will result is EXACTLY THE SAMEpoints.

3.4 Notes.notebook 8th feb 2013

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First re­write the equation intothe correct order. Note thatthe leading negative sign means"a" has a value of negative 1.

3.4 Notes.notebook 8th feb 2013

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February 08, 2013

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We need to do some practice to get ready for the final topic:

If the point (4,­6) is on f(x), then what would be the points according to the following transformation instructions:

a) (2x, y­3) ______________b) (x­3,2y) ______________c) (2x,2y) _______________d (x/2, y/3) _______________e) (2x+3,y/2 ­ 1) _______________

For each of the above, write a new expression for all of the points transformed by the instructions.ex: b) would become 2f(x+3) . The 2 would double the y values, and (x+3) would move all x values 3 to the left, thus decreasing their value by 3.

3.4 Notes.notebook 8th feb 2013

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February 08, 2013

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Writing the equation of a transformed graph.

Look at these graphs that show the original function f(x), and with dotted lines,the transformed function.Plot the points of both functions. What transformations caused the points of the original to become the transformed points. Remember they could be shifts or stretches (or both). Like we did in the previous examples, create a point transformation guide, and use it to write the equation.

f(x)

Now we are ready to tackle this:

3.4 Notes.notebook 8th feb 2013

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This example is very difficult because both x and y are BOTH stretched/compressed and then shifted.

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Homework: Page 226 #3,4,5,6,7a8a,9,10a, Mult ch. #1,2

Do Supplementary Sheet.