## Precalculus (10th Edition)

Published by Pearson

# Chapter 2 - Functions and Their Graphs - 2.5 Graphing Techniques: Transformations - 2.5 Assess Your Understanding - Page 103: 19

#### Answer

$f(x)=(x-4)^3$

#### 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: $x^3\rightarrow(x-4)^3.$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.