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

Name Date

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

2. f(x)=

2

3

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

4. 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.

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Copyright

©

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