Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - Chapter 2 Test Prep - Review Exercises - Page 299: 92

Answer

the x-axis, the y-axis, and the origin.

Work Step by Step

Step 1. To test symmetry with respect to the x-axis, replace $(x,y)$ with $(x,-y)$, we have: $|x|=|-y|$ which is the same as the original, thus it is symmetric with respect to the x-axis. Step 2. To test symmetry with respect to the y-axis, replace $(x,y)$ with $(-x,y)$, we have: $|-x|=|y|$ which is the same the original, thus it is symmetric with respect to the y-axis. Step 3. To test symmetry with respect to the origin, replace $(x,y)$ with $(-x,-y)$, we have: $|-x|=|-y|$ which is the same as the original, thus it is symmetric with respect to the origin. Step 4. Thus the equation has a symmetry with respect to the x-axis, the y-axis, and the origin.
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