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: 93

Answer

$f(x)=(x+3)(x+2)(x+1)(x-1)(x-2) $ See graph.
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Work Step by Step

Step 1. The end behavior can be identified as $x\to-\infty, y\to-\infty$ and $x\to\infty, y\to\infty$ Thus the leading coefficient should be positive and the power should be odd. Step 2. There are $4$ turning points. Thus we have $n=5$ as the degree of the polynomial. Step 3. We can write an example polynomial as $f(x)=(x+3)(x+2)(x+1)(x-1)(x-2)=(x+3)(x^2-4)(x^2-1) $ Step 4. See graph for the above function.
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