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: 75


Graph of the function as:

Work Step by Step

Substitute $x=-x$. $\begin{align} & f\left( x \right)=\frac{{{x}^{4}}}{{{x}^{2}}+2} \\ & f\left( -x \right)=\frac{{{\left( -x \right)}^{4}}}{{{\left( -x \right)}^{2}}+2} \\ & =\frac{{{x}^{4}}}{{{x}^{2}}+2} \\ & =f\left( x \right) \end{align}$ 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. Since the degree of the numerator is less than the denominator, there is no horizontal asymptote. For the vertical asymptote, equate the denominator to 0. Thus, there are no real asymptotes.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.