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 400: 94


$\frac{x^2-1}{x^2+1}$; see graph.

Work Step by Step

Step 1. Multiply the numerator and the denominator with $x$. We have $f(x)=\frac{x^2-1}{x^2+1}$ where $x\ne 0$ with a hole at $(0,-1)$ Step 2. There are no vertical asymptotes. Step 3. We can identify a horizontal asymptote as $y=1$ Step 4. We can find the x-intercepts at $(\pm1,0)$ Step 5. As $f(-x)=f(x)$, the function is symmetric with respect to the y-axis. Step 6. Based on the above results, we can graph the function as shown in the figure.
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