Precalculus (6th Edition) Blitzer

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

Chapter 2 - Section 2.5 - Zeros of Polynomial Functions - Exercise Set - Page 380: 97


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Work Step by Step

For a polynomial function of degree 20, we have the end behavior of either $x\to\pm\infty, y\to\infty$ or $x\to\pm\infty, y\to-\infty$, which means that the curve rises or falls on both the left and right sides. For this reason, if the curve crosses the x-axis, it must return and cross the x-axis again; in other words, it can not cross the x-axis exactly once.
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