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 430: 34

Answer

a. rises to the left and falls to the right. b. symmetric with respect to the origin. c. See graph.
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Work Step by Step

a. The leading term of the function $f(x)=-x^3+4x$ is $-x^3$, with a coefficient of $-1$ and an odd power. Thus, we can identify its end behaviors as $x\to-\infty, y\to\infty$ and $x\to\infty, y\to-\infty$. That is, the curve rises to the left and falls to the right. b. We test: $f(-x)=-(-x)^3+4(-x)=x^3-4x=-f(x)$ as $f(-x)=-f(x)$, the function is symmetric with respect to the origin. c. See graph.
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