Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.1 Polynomial Functions and Models - 4.1 Assess Your Understanding - Page 185: 63

Answer

(a) $x=-4$ (multiplicity 2) and $x=5$ (multiplicity 3). (b) $x=5$ crosses the x-axis, $x=4$ touches the x-axis. (c) $4$. (d) $y=x^5$.

Work Step by Step

(a) For $f(x)=(x-5)^3(x+4)^2$, we can list real zero as $x=-4$ (multiplicity 2) and $x=5$ (multiplicity 3). (b) At $x=5$ the graph crosses the x-axis, while at $x=4$ the graph touches the x-axis. (c) The maximum number of turning points on the graph is given by $n-1=5-1=4$. (d) As $n=5, a_5\gt0$, the end behaviors are rise to the right and fall to the left, similar to $y=x^5$.
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