Precalculus (6th Edition) Blitzer

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

Chapter 2 - Section 2.6 - Rational Functions and Their Graphs - Exercise Set - Page 399: 76

Answer

Graph the function as:
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Work Step by Step

Substitute $x=-x$. $\begin{align} & f\left( x \right)=\frac{2{{x}^{4}}}{{{x}^{2}}+1} \\ & f\left( -x \right)=\frac{2{{\left( -x \right)}^{4}}}{{{\left( -x \right)}^{2}}+1} \\ & =\frac{2{{x}^{4}}}{{{x}^{2}}+2} \\ & =f\left( x \right) \end{align}$ Therefore, the function $f\left( -x \right)$ is equal to $-f\left( x \right)$. The graph of the function is symmetric about the $y$ -axis and origin.
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