Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.5 - Transformations of Functions - 2.5 Exercises - Page 211: 28


a) $f(x)=|x|$ b) Horizontal shift to the left, vertical shift downward c) See graph d) $g(x)=f(x+3)-2$

Work Step by Step

We are given the function: $g(x)=|x+3|-2$ a) The parent function is: $f(x)=|x|$ b) Horizontally shift $f(x)$ 3 units to the left to get $a(x)=|x+3|$. Vertically shift $a(x)$ 2 units downward to get $g(x)=|x+3|-2$. c) Graph the transformations: d) Use function notation to write $g$ in terms of $f$: $g(x)=f(x+3)-2$
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