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


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.
Small 1564537613
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.