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: 73



Work Step by Step

If $c$ is a zero of a function with multiplicity $b$ then $(x-a)^b$ is a “factor” of the function. We can see from the graph that $0$, $1$ and $2$ are zeros of the function. Hence, $f(x)=a(x-0)(x−1)(x−2)\\ f(x)=a(x^3−3x^2+2x)$ When $a=1$, the function becomes $f(x)=x^3−3x^2+2x$ Thus, one possible polynomial function that might have the given graph is $f(x)=x^3−3x^2+2x$
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