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 212: 49b



Work Step by Step

Since the graph follows the shape $f(x)=|x|$ we will start with that equation: $f(x)=|x|$ First notice the graph is shifted down 3 units. Up and down shifts are added to the right side of the equation. Up is positive and down is negative: $f(x)=|x|-3$ Second, notice the graph has been stretched vertically (by a factor of k) and will follow the below equation: $f(x)=k|x|-3$ Substitute (-2,3) into the above equation to solve for k: $3=k|-2|-3$ $2k=6$ $k=3$ So we get the final function: $f(x)=3|x|-3$
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