the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the…

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, $a = 0$ and $b = 3$.

Step2: Find $f(0)$ and $f(3)$ from the graph

From the graph, when $x = 0$, $y=f(0)= - 20$. When $x = 3$, $y=f(3)=20$.

Step3: Calculate the average rate of change

Substitute $a = 0$, $b = 3$, $f(0)=-20$ and $f(3)=20$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(3)-f(0)}{3 - 0}=\frac{20-(-20)}{3}=\frac{20 + 20}{3}=\frac{40}{3}$.

Answer:

$\frac{40}{3}$