Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 2 - Functions and Their Graphs - 2.5 Graphing Techniques: Transformations - 2.5 Assess Your Understanding - Page 104: 57


See graph

Work Step by Step

We are given the function: $f(x)=-(x+1)^3-1$ We start graphing with the basic function $a(x)=x^3$. We horizontally shift $a(x)$ one unit to the left to get $b(x)=(x+1)^3$. Then we reflect $b(x)$ about the $x$-axis to get $c(x)=-(x+1)^3$. Finally we vertically shift $c(x)$ one unit downward to get $f(x)=-(x+1)^3-1$. We use 4 points: $(-2,0),(-1,-1),(0,-2)$.
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