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: 57

Answer

(a) $x=7$ (multiplicity 1) and $x=-3$ (multiplicity 2). (b) $x=7$ crosses the x-axis, $x=-3$ touches the x-axis. (c) $2$. (d) $y=3x^3$.

Work Step by Step

(a) For $f(x)=3(x-7)(x+3)^2$, we can list real zero as $x=7$ (multiplicity 1) and $x=-3$ (multiplicity 2). (b) At $x=7$ the graph crosses the x-axis, while at $x=-3$ the graph touches the x-axis. (c) The maximum number of turning points on the graph is given by $n-1=3-1=2$. (d) As $n=3, a\gt0$, the end behaviors are rise to the right and fall to the left similar to $y=3x^3$.
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