University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 2 - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises - Page 108: 71


The graph of $y=f(x)$ is sketched below.

Work Step by Step

The graph of the function $y=f(x)$ is sketched below. - $f$ passed the point $(0,0)$. - As $x$ approaches $-1^+$ and $1^-$, $f$ both approaches $\infty$, so we pull 2 lines from $(0,0)$ to $\infty$ as $x\to1$ and $x\to-1$. - As $x$ approaches $-1^-$ and $1^+$, $f$ both approaches $-\infty$, so we would start 2 new lines from $-\infty$ on the left of $-1$ and on the right of $1$. - As $x$ approaches $\pm\infty$, $f$ approaches $0$, so we pull these 2 new lines both towards $0$ as $x$ becomes infinitely large.
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