Name Date
WORKSHEET 8.5: DESCRIBING REFLECTIONS OF THE GRAPH
OF A FUNCTION
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Equations can be used to show reflections of the graphs of a function. Follow the steps below:
- Find the basic function the equation describes.
- Compare the equation toy=f(x).
- The graph ofy=−f(x)is the reflection off(x)in thex-axis.
- The graph ofy=f(−x)is the reflection off(x)in they-axis.
EXAMPLE
Describe the graphs off(x)=−|x|andg(x)=|−x|.
The graph off(x)is the reflection of the absolute value function in thex-axis. The graph of
g(x)is the reflection of the absolute value function in they-axis.
DIRECTIONS: Describe the graph of each function.
- f(x)=−x^2 2. g(x)=−
(
1
x
)
- F(x)=(−x)^3
- h(x)=(−x)^2 5. j(x)=−x 6. I(x)=−(x)^3
CHALLENGE:Explain why the graph ofy=x^2 looks exactly like the graph of
y=(−x)^2.
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Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.