College Algebra, Chapter 3, 3.4, Section 3.4, Problem 12

A function $\displaystyle f(z) = 1 - 3z^2$. Determine the average rate of change of the function between $z = -2$ and $z = 0$.


$\begin{equation} \begin{aligned} \text{average rate of change } =& \frac{f(b) - f(a)}{b - a} && \text{Model} \\ \\ \text{average rate of change } =& \frac{f(0) - f(-2)}{0 - (-2)} && \text{Substitute } a = -2 \text{ and } b = 0 \\ \\ \text{average rate of change } =& \frac{1 - 3(0)^2 - [1 - 3(-2)^2]}{2} && \text{Simplify} \\ \\ \text{average rate of change } =& \frac{1 - 1 + 12}{2} && \text{Combine like terms} \\ \\ \text{average rate of change } =& \frac{12}{2} && \text{Simplify} \\ \\ \text{average rate of change } =& 6 && \text{Answer} \end{aligned} \end{equation}$