## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 2 - 2.5 - Transformations of Functions - 2.5 Exercises - Page 211: 35

#### Answer

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

#### Work Step by Step

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

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