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: 38


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

Work Step by Step

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