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

(Marvins-Underground-K-12) #1

Teaching Notes 8.5: Describing Reflections of the Graph


of a Function


Equations describe the reflections of the graph of a function. Students may confuse reflections in
they-axis with reflections in thex-axis because of where the negative sign is placed in the
equation.


  1. Show the graphs of the following basic functions to your students. Label each graph with the
    name of the function.


Identity:f(x)=x Squaring:f(x)=x^2 Cubing:f(x)=x^3

Square root:f(x)=


x Absolute value:f(x)=|x| Reciprocal:f(x)=

1

x


  1. Explain that the graphs of functions may be reflected in they-axis and in thex-axis. Note
    that when a graph of a function is reflected, the size and shape of the graph remains the
    same.

  2. Consider the graph of the square root functionf(x)=



x. Then sketch the graphs ofg(x)=


xandh(x)=


−x. Note that the size and shape of all the graphs are the same.g(x)is
the reflection off(x)inthex-axis andh(x) is the reflection off(x)inthey-axis.


  1. Review the information and example on the worksheet with your students. For the example,
    emphasize that students must identify the basic function and then determine the axis in
    which the graph is reflected. Note that the domains of the functions are restricted so that
    the functions are defined.


EXTRA HELP:
The graph of the opposite of a function is a reflection of the graph of the function in thex-axis.
The graph of the opposite ofxis a reflection of the graph of the function in they-axis.

ANSWER KEY:
The graph shows the following:

(1)Squaring function reflected in thex-axis (2)Reciprocal function reflected in thex-axis
(3)Cubing function reflected in they-axis (4)Squaring function reflected in they-axis
(5)Identity function reflected in they-axis (6)Cubing function reflected in thex-axis
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(Challenge)Thegraphslookthesamebecausewhenthegraphofy=x^2 is reflected in the
y-axis, the graphs coincide.
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282 THE ALGEBRA TEACHER’S GUIDE

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