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: 28

Answer

From the far left to the far right, the graph - rises from $-\infty$, the lower far left, - flattens out near $(-2,0)$ where it crosses the x-axis, - continues to rise above y=8 before it turns and - crosses the y-axis at $(0,8)$, falling to - to the point $(-1,0)$, where it touches x and turns back, rising - and continues to rise to the far right.

Work Step by Step

End behavior: When $ x\rightarrow-\infty$ , the squared factor is positive, the cubed is negative $P(x)$ is negative to the far left. When $ x\rightarrow+\infty$ , both factors are positive, $P(x)$ is positive to the far right. Intercepts: $ x-1=0,\quad x+2=0$ x-intercepts: $x=-2,$ triple (graph flattens out at the crossing)$.\\\\$ $x=1$, double (graph touches x and turns)$.\\\\$ y-intercept: $P(0)=(-1)^{2}(2^{3})=8$ $P(0.5)\approx 3.9$, so the graph falls through $(0,8)$ From the far left to the far right, the graph - rises from $-\infty$, the lower far left, - flattens out near $(-2,0)$ where it crosses the x-axis, - continues to rise above y=8 before it turns and - crosses the y-axis at $(0,8)$, falling to - to the point $(-1,0)$, where it touches x and turns back, rising - and continues to rise to the 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.