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 - Page 20: 65

Answer

$y=1-{27}x^3$

Work Step by Step

Given the graph of $y=f(x)$ and a real number $c>1$, we obtain the graph of $y=f\left({c}x\right)$ 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 3, we replace each occurrence of $x$ in this equation by ${3}x$ obtaining the equation $$y=1-\left({3}x\right)^3,$$ or equivalently, $$y=1-{27}x^3.$$
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