what is the average rate of change in f(x) over the interval 4,13? 1/3 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, $a = 4$, $b = 13$. From the graph, when $x = 4$, $f(4)=8$; when $x = 13$, $f(13)=11$.

Step2: Substitute values into formula

$\frac{f(13)-f(4)}{13 - 4}=\frac{11 - 8}{13 - 4}$.

Step3: Calculate the result

$\frac{11 - 8}{13 - 4}=\frac{3}{9}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$