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: 36


a) $f(x)=x^2$ b) Vertical shrink, vertical shift c) See graph d) $g(x)=\dfrac{1}{2}f(x)-2$

Work Step by Step

We are given the function: $g(x)=\dfrac{1}{2}x^2-2$ a) The parent function is: $f(x)=x^2$ b) Vertically shrink $f(x)$ by a factor of $\dfrac{1}{2}$ to get $a(x)=\dfrac{1}{2}x^2$. Vertically shift $a(x)$ 2 units downward to get $g(x)=\dfrac{1}{2}x^2-2$. c) Graph the transformations. d) Use function notation to write $g$ in terms of $f$: $g(x)=\dfrac{1}{2}f(x)-2$
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