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: 20

Answer

Refer to the graph below.
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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-3&=0 &\text{or}& &x+2=0& &\text{or}& &3x-2=0\\ x&=3 &\text{or}& &x=-2& &\text{or}& &3x=2\\ x&=3 &\text{or}& &x=-2& &\text{or}& &x=\frac{2}{3}\\ \end{align*} Thus, the $x$-intercepts are $-2, \frac{2}{3},$ and $3$. The $y$_intercept of the function can be found by setting $x=0$ then solving for $y$: \begin{align*} P(0)&=(0-3)(0+2)(3\cdot0-2)\\ P(0)&=-3(2)(-2)\\ P(0)&=12 \end{align*} Thus, the $y$-intercept is $12$ 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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