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: 15

Answer

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Work Step by Step

Since $(x-1)$ and $(x+2)$ are factors of $P(x)$, then x-intercepts: $x=1, x=-2$ (both multiplicity 1, the graph crosses over the x-axis). P(0)=$(-1)(2)=-2$ (y-intercept) P(0.1)=-1.89, so the graph rises as it crosses the y-axis. End behavior: When $ x\rightarrow-\infty$ , both factors are negative so $ P(x)\rightarrow+\infty$ When $ x\rightarrow+\infty$ , both factors are positive so $ P(x)\rightarrow+\infty$ Description of the graph in words, from left to right: - it falls from the high upper left, - crosses the x-axis at $x=-2$, - continues falling to a minimum point (before the origin, below y=-2), - after reaching the minimum point, turns upward and crosses the y-axis at x=-2, - continues rising, crosses the x-axis at x=1, and - continues to rise indefinitely.
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