## Thomas' Calculus 13th Edition

Published by Pearson

# Chapter 1: Functions - Section 1.2 - Combining Functions; Shifting and Scaling Graphs - Exercises 1.2 - Page 20: 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, $$y=1-\dfrac{1}{8}x^3.$$

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