Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.9 - Distance and Midpoint Formulas; Circles - Exercise Set - Page 282: 98

Answer

Symmetric with respect to the y-axis. Not symmetric with respect to the x-axis or the origin (see graph).
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Work Step by Step

Step 1. Rewrite the equation as $f(x)=y=(x^2-2)^{1/3}$ Step 2. Test $f(-x)=((-x)^2-2)^{1/3}=(x^2-2)^{1/3}=f(x)$ Step 3. We can conclude that $f(x)$ is an even function and is symmetric with respect to the y-axis. The function is not symmetric with respect to the x-axis or the origin (see graph).
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