College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.1 - Polynomial Functions and Models - 5.1 Assess Your Understanding - Page 340: 85

Answer

Check graph

Work Step by Step

$f(x) = -2(x + 2)(x - 2)^3$ Step 1. $f(x) = -2x^4 + 8x^3 - 32x + 32$ is a degree 4 polynomial End behavior as $y = -2x^4$ for large x Step 2. Y-Intercept = $f(0) = 32$ X-Intercept when $f(x) = 0$ gives $x = -2, 2$ Step 3. Zeros of the function are $x = -2, 2$ Multiplicity of Zero -2 is 1(odd) so the graph of f crosses the x-axis at x = -2. Multiplicity of Zero 2 is 3(odd) so the graph of f crosses the x-axis at x = 2. Step 4. Because the polynomial function is of degree 3 (Step 1), the graph of the function will have at most 4 - 1 = 3 turning points. But since root $x = 2$ is triply repeated, there will be inflection point at $x = 2$ and only single turning point Step 5. Finding values of f(x) for some x and plotting the graph using results of step 1 to 4 $f(1) = 6$, $f(-1) = 54$, $f(0) = 32$, $f(3) = -10$
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