College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.5 - Graphing Techniques: Transformations - 3.5 Assess Your Underdstanding - Page 258: 38

Answer

$a.\quad (-4,5).$ $b.\quad (3,12)$ $c.\quad -f(x)$ decreases on $(-2,7)$ $d.\quad f(-x)$ decreases on $(-7,2)$

Work Step by Step

$a.$ The graph of f(x) is translated to the left by $2$ units, so the interval of increase is now $(-2-2,7-2)=(-4,5)$ $b.$ The graph of f(x) is translated to the right by $5$ units, so the interval of increase is now $(-2+5,7+5)=(3,12)$ $c.$ The graph of f(x) is reflected about the x-axis, so it now decreases where it used to increase. $-f(x)$ decreases on $(-2,7)$ $d.$ The graph of f(x) is reflected about the y-axis, so it now decreases on an interval corresponding to the one where it used to increase. The borders of the interval were also reflected, so $f(-x)$ decreases on $(-7,2)$
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