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: 81

Answer

See picture attached

Work Step by Step

$f(x) = x^2(x - 3)$ Step 1. $f(x) = x^3 -3x$ is a degree 3 polynomial End behavior as $y = x^3$ for large x Step 2. Y-Intercept = $f(0) = 0$ X-Intercept when $f(x) = 0$ gives $x = 0, 3$ Step 3. Zeros of the function are $x = 0, 3$ Multiplicity of Zero 0 is 2(even) so the graph of f touches the x-axis at x = 0. Multiplicity of Zero 3 is 1(odd) so the graph of f crosses the x-axis at $x = 3$. Step 4. Because the polynomial function is of degree 3 (Step 1), the graph of the function will have at most 3 - 1 = 2 turning points. Step 5. Finding values of f(x) for some x and plotting the graph using results of step 1 to 4 $f(1) = -2$, $f(-1) = -4$, $f(2) = -4$, $f(4) = 16$
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