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

(Marvins-Underground-K-12) #1
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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:


  1. Find the basic function the equation describes.

  2. 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.



  1. f(x)=−x^2 2. g(x)=−


(

1

x

)


  1. F(x)=(−x)^3

  2. 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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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.

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