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: 37


a) $f(x)=|x|$ b) Horizontal shift, vertical stretch, vertical shift c) See graph d) $g(x)=3f(x-1)+2$

Work Step by Step

We are given the function: $g(x)=3|x-1|+2$ a) The parent function is: $f(x)=|x|$ b) Horizontally shift $f(x)$ one unit to the right to get $a(x)=|x-1|$. Vertically stretch $a(x)$ by a factor of 3 to get $b(x)=3|x-1|$. Vertically shift $b(x)$ 2 units upward to get $g(x)=3|x-1|+2$. c) Graph the transformations. d) Use function notation to write $g$ in terms of $f$: $g(x)=3f(x-1)+2$
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