Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Section 3.1 Polynomial Functions and Models - 3.1 Assess Your Understanding - Page 210: 87

Answer

Step 1: $y=x^3$ Step 2: $x=0,1,2$, $f(0)=0$. Step 3: $x=0,1,2$ (multiplicity 1, crosses the x-axis), Step 4: $2$. Step 5: See graph.

Work Step by Step

Step 1: Given $f(x)=x(1-x)(2-x)=x(x-1)(x-2)$, we can determine the end behavior as similar to $y=x^3$ Step 2: For x-intercept(s), let $f(x)=0$, we have $x=0,1,2$, for y-intercept(s), let $x=0$, we have $f(0)=0$. Step 3: We can determine the zeros $x=0,1,2$ (multiplicity 1, crosses the x-axis), Step 4: The maximum number of turning points is $n-1=3-1=2$. Step 5: See graph.
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