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: 66


The equation of the stretched graph is $$y=\frac{8-x^3}{8}$$

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 $c$ $$y=1-x^3$$ The graph is STRETCHED - HORIZONTALLY - by a factor of $2$. Therefore, the equation of the new graph is $$y=1-\Big(\frac{x}{2}\Big)^3$$ $$y=1-\frac{x^3}{8}$$ $$y=\frac{8-x^3}{8}$$
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