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: 17

Answer

please see image:

Work Step by Step

End behavior: When $ x\rightarrow-\infty$ , observing just the signs, we have $-(-)(-)(-)$, so $ P(x)\rightarrow+\infty$ When $ x\rightarrow+\infty$ , observing just the signs, we have $-(+)(+)(+)$, so $ P(x)\rightarrow-\infty$ Intercepts: x-intercepts: $x=-2, x=0, x=3.$ y-intercept: $P(0)=0$ Short description of the graph, left to right: - falls from the upper left, - crosses the x-axis at x=-2, - continues falling to a local minimum, turns and - while rising, crosses the x-axis at the origin, - continues rising to a local maximum, turns, and - while falling, crosses the x-axis at x=3, - continues falling indefinitely
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