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

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

2. 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.


3. 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.

4. 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