Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 2 - Review - Exercises - Page 231: 12

Answer

a) $f(-2)=-1$ , $f(2)=2$ b) Net change: +$3$ Avg. rate of change: $\frac{3}{4}$ c) Domain: [-4, 5], Range: [-4, 4] d) The intervals when the function is increasing are [-4, -2) and (-1, 4). The intervals when the function is decreasing are (-2,-1) and (4, 5] e) The local maximum values are $-1$ and $4$. f) No

Work Step by Step

a) Looking at the graph, one can find that $f(-2)=-1$ and $f(2)=2$ b) Net change: $f(2)-f(-2)=2-(-1)=+3$ The positive answer means there was an increase Avg. rate of change: $\frac{f(2)-f(-2)}{2-(-2)}=\frac{2-(-1)}{4}=\frac{3}{4}$ c) The domain is an interval of the total extension in a horizontal point of view of the function, while the range is an interval of the total extension from a vertical point of view of the function. d) A function decreases when the slope is negative. While a function increases when the slope is positive. e) The local maximum values are all those that are at the top of crests that forms in the function. f) One can check if a function is one-to-one by applying the horizontal test. In the graph, one can see that in the domain (-3, 0.5), more than one point intersects the imaginary horizontal line.
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