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: 64


$$y=\dfrac{1}{3}\sqrt{4-x^2},$$ or equivalently, $$y=\sqrt{\dfrac{4}{9}-\dfrac{x^2}{9}}$$

Work Step by Step

Given the graph of $y=f(x)$ and a real number $c>1$, we obtain the graph of $y=\dfrac{1}{c}f(x)$ by vertically compressing the graph of $y=f(x)$ by a factor of $c$. Hence to vertically compress the graph of $y=\sqrt{4-x^2}$ by a factor of 3, we multiply the right hand side of this equation by $\dfrac{1}{3}$ and, thus, obtain $$y=\dfrac{1}{3}\sqrt{4-x^2},$$ or equivalently, $$y=\sqrt{\dfrac{4}{9}-\dfrac{x^2}{9}}.$$
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