Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -2 ≤ x ≤ 6?

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$ and $b = 6$.

Step2: Find $f(-2)$ and $f(6)$ from the graph

From the graph, when $x=-2$, $f(-2)=20$. When $x = 6$, $f(6)=-15$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(6)-f(-2)}{6-(-2)}=\frac{-15 - 20}{6 + 2}=\frac{-35}{8}=-\frac{35}{8}$.

Answer:

$-\frac{35}{8}$