## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 5 - Review Exercises - Page 412: 20

#### Answer

A horizontal shift of $2$ to the right and then a reflection about the x-axis.

#### Work Step by Step

RECALL: (1) The graph of $y=f(x-h)$ involves a horizontal shift of $|h|$ units (to the right when $h \gt 0$, to the left when $h\lt0$) of the parent function $f(x)$. (2) The graph of $y=f(x)+k$ involves a vertical shift of $|k|$ units (upward when $k \gt 0$, downward when $k\lt0$) of the parent function $f(x)$. (3) The graph of $y=a \cdot f(x-h)$ involves a vertical stretch or compression (stretch when $a\gt1$, compression when $0\lt a \lt1$) of the parent function $f(x)$. (4) The graph of $y=-f(x)$ involves a reflection about the $x$-axis of the parent function $f(x)$. Hence here $g$ is obtained by a horizontal shift of $2$ to the right and then a reflection about the x-axis.

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