Precalculus (6th Edition) Blitzer

Published by Pearson

Chapter 4 - Cumulative Review Exercises - Page 647: 12

Answer

See graph and explanations.

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.

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