Answer
True.
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.
