Precalculus (6th Edition) Blitzer

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

Chapter 1 - Test - Page 306: 24

Answer

The function is only symmetric with respect to the y-axis.
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Work Step by Step

Step 1. Replacing $x$ with $-x$, we have $(-x)^2+y^3=7$, which gives $x^2+y^3=7$; thus the function is symmetric with respect to the y-axis. Step 2. Replacing $y$ with $-y$, we have $x^2+(-y)^3=7$, which gives $x^2-y^3=7$; thus the function is not symmetric with respect to the x-axis. Step 3. Replacing $x$ with $-x$ and $y$ with $-y$, we have $(-x)^2+(-y)^3=7$, which gives $x^2-y^3=7$; thus the function is not symmetric with respect to the origin.
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