Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 2 - Section 2.3 - Getting Information from the Graph of a Function - 2.3 Exercises - Page 180: 34

Answer

(a) Domain: $[-2,2]$ Range: $[-2,2]$ (b) Increasing: $(-1,1)$ Decreasing: $(-2,-1)$, $(1,2)$

Work Step by Step

(a) To estimate the domain, we look at the x-values that the function takes on in the graph. We can see that the x-values span from -2 to 2 and the endpoints are included. Thus the domain is: $[-2,2]$ To estimate the range, we look at y-values. The y-values span from -2 to 2, including endpoints. Thus the range is: $[-2,2]$ (b) We notice the x-values of where the function is increasing from left to right: $(-1,1)$ Similarly, we notice where the function is decreasing: $(-2,-1)$, $(1,2)$ Note that we do not include the end points, since the function has discontinuities there and is neither increasing nor decreasing.
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