The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

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WORKSHEET 8.8: DESCRIBING DILATIONS OF THE GRAPH OF A
FUNCTION
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Equations may be used to show a vertical stretch or a compression of the graph of a function.
Follow the steps below:


  1. Find the basic function the equation describes.

  2. Compare the equation toy=af(x).

    • Ifa>1, the graph is stretched away from thex-axis.

    • If 0<a<1, the graph is compressed (or shrunk) toward thex-axis.

    • Ifa= 1 , there is no dilation.




EXAMPLE
Describe the graphs off(x)= 6 |x|andh(x)=
|x|
6

.

The graph off(x)is the graph of the absolute value function. Becausea= 6 , which is greater
than 1, it is stretched away from thex-axis. The graph ofh(x)is also the graph of the absolute
value function. But becausea=

1

6

, which is greater than 0 and less than 1, it is compressed
toward thex-axis.

DIRECTIONS: Describe the graph of each function.



  1. g(x)=


2

x


  1. f(x)=


2

3

|x| 3. h(x)= 2 x^3



  1. j(x)=
    x
    2
    5. I(x)= 4 x^2 6. F(x)=


2

5


x

CHALLENGE:Louis described the graph off(x)=− 2 |x|as the absolute value
function reflected over thex-axis and stretched away from thex-axis. Is he
correct? Explain your reasoning.

289

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©


2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.

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