Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.2 - Polynomial Functions and Their Graphs - 3.2 Exercises - Page 266: 20

Answer

From the far left to the far right, the graph - rises from $-\infty$ on the far left, - crosses the x-axis at $(-2,0),$ rising - continues to rise above 12, turns, and - falling, crosses the y-axis at y=12, - falls through $(\displaystyle \frac{2}{3},0)$ below the x-axis, - turns back rising through $(3,0),$ - continues rising to the upper far right.

Work Step by Step

End behavior: When $ x\rightarrow-\infty$ , all three factors are negative. $P(x)$ is negative to the far left. When $ x\rightarrow+\infty$ , all three factors are positive. $P(x)$ is positive to the far right. Intercepts: $x-3=0,\quad x+2=0\qquad 3x-2=0$ x-intercepts: at $x=3, x=-2$, and $x=\displaystyle \frac{2}{3}$, all single$.\\\\$ y-intercept: $P(0)=-3(2)(-2)=+12$ Behavior around the y-intercept: $P(-1)=20, P(0)=12, P(1)=6,$ so the graph falls through the y-intercept From the far left to the far right, the graph - rises from $-\infty$ on the far left, - crosses the x-axis at $(-2,0),$ rising - continues to rise above 12, turns, and - falling, crosses the y-axis at y=12, - falls through $(\displaystyle \frac{2}{3},0)$ below the x-axis, - turns back rising through $(3,0),$ - continues rising to the upper far right.
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.