Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 15

Answer

(a) $-2,3$. (b) $(-\infty,-2]\cup[3,\infty)$. (c) $(-2,3)$.

Work Step by Step

(a) Use the given graph, we can identify the intersects $(-2,5),(3,5)$, thus the solutions to $f(x)=g(x)$ are $x=-2,3$. (b) $f(x)\ge g(x)$ happens when $x\le-2$ or $x\ge3$, that is $(-\infty,-2]\cup[3,\infty)$. (c) $f(x)\lt g(x)$ happens when $-2\lt x\lt3$ or $(-2,3)$.
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