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:
- Find the basic function the equation describes.
- 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.
- g(x)=
2
x
- f(x)=
2
3
|x| 3. h(x)= 2 x^3
- 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.