what is the average rate of change in f(x) over the interval 4,13?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$ and $b=13$.

Step2: Find $f(4)$ and $f(13)$ from the graph

From the graph, when $x = 4$, $f(4)=8$; when $x = 13$, $f(13)=11$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(13)-f(4)}{13 - 4}=\frac{11 - 8}{9}=\frac{3}{9}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$