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 $b=2$.

Step2: Read function values from the graph

From the graph, when $x = 0$, $f(0)=1$; when $x = 2$, $f(2)=16$.

Step3: Calculate the average rate of change

Substitute $a = 0$, $b = 2$, $f(0)=1$, and $f(2)=16$ into the formula: $\frac{f(2)-f(0)}{2 - 0}=\frac{16 - 1}{2}=\frac{15}{2}$.

Answer:

$\frac{15}{2}$