Precalculus (6th Edition) Blitzer

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

Chapter 4 - Cumulative Review Exercises - Page 647: 12

Answer

See graph and explanations.
1583720346

Work Step by Step

Step 1. Given the function $f(x)=\frac{x}{x^2-1}=\frac{x}{(x+1)(x-1)}$ we can identify two vertical asymptotes as $x=\pm1$ Step 2. We can identify a horizontal asymptote as $y=0$ Step 3. The x-intercept is $x=0$ and the y-intercept is $y=0$ Step 4. Testing signs across the vertical asymptotes and $x=0$, we have: $...(-)...(-1)...(+)...(0)...(-)...(1)...(+)...$ Step 5. Testing for symmetry, $f(-x)=-f(x)$, the function is odd and symmetric with respect to the origin. Step 6. Use the above results and test points if necessary to obtain a graph as shown in the figure.
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.