the graph of a function f is shown below. use the graph of the function to find its average rate of change…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$ and $b = 4$.

Step2: Determine $f(0)$ and $f(4)$ from the graph

From the graph, when $x = 0$, $f(0)=2$; when $x = 4$, $f(4)=16$.

Step3: Calculate the average rate of change

Substitute $f(0)=2$, $f(4)=16$, $a = 0$, and $b = 4$ into the formula: $\frac{f(4)-f(0)}{4 - 0}=\frac{16 - 2}{4}=\frac{14}{4}=\frac{7}{2}$.

Answer:

$\frac{7}{2}$