University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.2 - Combining Functions; Shifting and Scaling Graphs - Exercises - Page 20: 63


The equation of the stretched graph is $$y=\frac{\sqrt{16-x^2}}{2}$$

Work Step by Step

For $c\gt1$, the graph is scaled: - $y=cf(x)$ - stretched - vertically - factor of $c$ - $y =\frac{1}{c}f(x)$ - compressed - vertically - factor of $c$ - $y=f(cx)$ - compressed - horizontally - factor of $c$ - $y=f(\frac{x}{c})$ - stretched - horizontally - factor of $c$ $$y=\sqrt{4-x^2}$$ The graph is STRETCHED - HORIZONTALLY - by a factor of $2$. Therefore, the equation of the new graph is $$y=\sqrt{4-\Big(\frac{x}{2}\Big)^2}$$ $$y=\sqrt{4-\frac{x^2}{4}}$$ $$y=\sqrt{\frac{16-x^2}{4}}$$ $$y=\frac{\sqrt{16-x^2}}{2}$$
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