Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.2 Properties of Rational Functions - 4.2 Assess Your Understanding - Page 199: 69

Answer

symmetric with respect to the x-axis only.

Work Step by Step

Step 1. To test for x-axis symmetry, replace $(x,y)$ with $(x,-y)$, we see the equation is unchanged, thus it is symmetric with respect to the x-axis. Step 2. To test for y-axis symmetry, replace $(x,y)$ with $(-x,y)$, we see the equation is changed, thus it is not symmetric with respect to the y-axis. Step 3. To test for origin symmetry, replace $(x,y)$ with $(-x,-y)$, we see the equation is changed, thus it is not symmetric with respect to the origin.
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