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

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:

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

)

3. F(x)=(−x)^3


4. 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

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