Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -1 ≤ x ≤ 2?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$ and $b = 2$.

Step2: Find $f(-1)$ and $f(2)$ from the graph

From the graph, when $x=-1$, $f(-1)= - 10$; when $x = 2$, $f(2)=-20$.

Step3: Calculate the average rate of change

Substitute $a=-1$, $b = 2$, $f(-1)=-10$ and $f(2)=-20$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(2)-f(-1)}{2-(-1)}=\frac{-20-(-10)}{2 + 1}=\frac{-20 + 10}{3}=\frac{-10}{3}=-\frac{10}{3}$.

Answer:

$-\frac{10}{3}$