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: 46


See graph Domain: $(-\infty,\infty)$ Range: $(-\infty,\infty)$

Work Step by Step

We are given the function: $f(x)=(x+2)^3-3$ We start with the basic function $a(x)=x^3$. We horizontally shift $a(x)$ 2 units to the left to get $b(x)=(x+2)^3$. Then we vertically shift $b(x)$ 3 units downward to get $f(x)=(x+2)^3-3$. We use 3 points: $(-2,-3),(-1,-2),(0,5)$ The domain of $f$ is: $D=(-\infty,\infty)$ The range of $f$ is: $R=(-\infty,\infty)$
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