College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 3, Polynomial and Rational Functions - Section 3.2 - Polynomial Functions and Their Graphs - 3.2 Exercises - Page 302: 28

Answer

Refer to the graph below.

Work Step by Step

The $x$-intercepts of the function's graph can be found by equating each factor to zero then solving each equation to obtain: \begin{align*} (x-1)^2&=0 &\text{or}& &(x+2)^3=0\\ x-1&=\pm\sqrt0 &\text{or}& &x+2=\sqrt[3]0\\ x-1&=0 &\text{or}& &x+2=0\\ x&=1 \text{ (multiplicity 2)} &\text{or}& &x=-2 \\ \end{align*} Thus, the $x$-intercepts are $-2 \text{ and } 1$. The $y$-intercept of the function can be found by setting $x=0$ then solving for $y$: \begin{align*} P(0)&=(0-1)^2(0+2)^3\\ &=(-1)^2(2^3)\\ &=1(8)\\ &=8 \end{align*} Thus, the $y$-intercept is $8$. Create a table of values to obtain the one below. Then, plot each ordered pair and connect the points using a smooth curve. Refer to the graph above.
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