Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 6 - Transformations of Functions and Their Graphs - Strengthen Your Understanding - Page 263: 14



Work Step by Step

The rate of change over two x-values $x_1$ and $x_2$ can be written as $$\frac{f(x_2)-f(x_1)}{x_2-x_1}$$ If $f(x)$ becomes $kf(x)$, the rate of change now becomes $$\frac{kf(x_2)-kf(x_1)}{x_2-x_1}=k\left(\frac{f(x_2)-f(x_1)}{x_2-x_1}\right)$$ Therefore, the statement is true.
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