Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -3 ≤ 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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-3$ and $b = 2$.

Step2: Find $f(-3)$ and $f(2)$ from the graph

From the graph, when $x=-3$, $f(-3)=-8$. When $x = 2$, $f(2)=8$.

Step3: Calculate the average rate of change

Substitute $f(-3)=-8$, $f(2)=8$, $a=-3$, and $b = 2$ into the formula: $\frac{f(2)-f(-3)}{2-(-3)}=\frac{8-(-8)}{2 + 3}=\frac{8 + 8}{5}=\frac{16}{5}=3.2$.

Answer:

$3.2$