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: 65


The equation of the compressed graph is $$y=1-27x^3$$

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 COMPRESSED - HORIZONTALLY - by a factor of $3$. Therefore, the equation of the new graph is $$y=1-(3x)^3$$ $$y=1-27x^3$$
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