Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Section 1.2 - Combining Functions; Shifting and Scaling Graphs - Exercises 1.2: 65

Answer

$y=1-\dfrac{1}{8}x^3$

Work Step by Step

Given the graph of $y=f(x)$ and a real number $c>1$, we obtain the graph of $y=f\left(\dfrac{1}{c}x\right)$ by horizontally compressing the graph of $y=f(x)$ by a factor of $c$. Hence to horizontally compress the graph of $y=1-x^3$ by a factor of 2, we replace each occurrence of $x$ in this equation by $\dfrac{1}{2}x$ obtaining the equation $$y=1-\left(\dfrac{1}{2}x\right)^3,$$ or equivalently, $$y=1-\dfrac{1}{8}x^3.$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

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.