Precalculus (6th Edition) Blitzer

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

Chapter 2 - Section 2.3 - Polynomial Functions and Their Graphs - Exercise Set - Page 352: 97

Answer

The graph of the given polynomial function $ f\left( x \right)=-{{x}^{5}}+5{{x}^{4}}-6{{x}^{3}}+2x+20$ is shown below:

Work Step by Step

We know that according to the Leading Coefficient Test, the end behavior of the graph of a polynomial function, $ g\left( x \right)={{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+\cdots +{{a}_{2}}{{x}^{2}}+{{a}_{1}}x+{{a}_{0}}$ depends on the leading coefficient $\left( {{a}_{n}} \right)$ and the degree of the polynomial. We use the rules given on page 337 to graph the polynomial. Here, the polynomial function has degree 5 (odd) and its leading coefficient is negative, so the graph will fall at the right end and rise at the left end.
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