Precalculus (10th Edition)

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

Chapter 2 - Functions and Their Graphs - 2.3 Properties of Functions - 2.3 Assess Your Understanding - Page 78: 3

Answer

symmetric with respect to the $y$-axis.

Work Step by Step

Step 1. To test $x$-axis symmetry, replace $(x,y)$ with $(x,-y)$, we have $-y=5x^2-1$ which is equivalent to $y=-5x^2+1$. This is different from the original equation, thus it is not symmetric with respect to the $x$-axis. Step 2. To test $y$-axis symmetry, replace $(x,y)$ with $(-x,y)$, we have $y=5(-x)^2-1$, which is equivalent to $y=5x^2-1$, the original equation. Thus, the function's grap is symmetric with respect to the $y$-axis. Step 3. To test origin symmetry, replace $(x,y)$ with $(-x,-y)$, we have $-y=5(-x)^2-1$ which when simplified becomes $y=-5x^2+1$. This is different from the original equation, thus it is not symmetric with respect to the origin
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