Precalculus (6th Edition) Blitzer

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

Chapter 2 - Review Exercises - Page 431: 77

Answer

no vertical asymptote. no horizontal asymptote. slant asymptote: $y=-2x$ See graph.
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Work Step by Step

Step 1. Rewrite the function as $f(x)=\frac{-2x^3}{x^2+1}=\frac{-2x^3-2x+2x}{x^2+1}=-2x+\frac{2x}{x^2+1}$ Step 2. There is no vertical asymptote. Step 3. There is no horizontal asymptote. Step 4. A slant asymptote can be found as $y=-2x$ Step 5. See graph.
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