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: 26


a) $f(x)=x^2$ b) Horizontal shift one unit to the right, reflection across the $x$-axis, vertical shift upward c) See graph d) $g(x)=-f(x-2)+4$

Work Step by Step

We are given the function: $g(x)=4-(x-2)^2$ a) The parent function is: $f(x)=x^2$ b) Horizontally shift $f(x)$ 2 units to the right to get $a(x)=(x-2)^2$. Reflect $a(x)$ across the $x$-axis to get $b(x)=-(x-2)^2$. Vertically shift $b(x)$ 4 units upward to get $g(x)=4-(x-2)^2$. c) Graph the transformations: d) Use function notation to write $g$ in terms of $f$: $g(x)=-f(x-2)+4$
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