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, $a = 5$ and $b=7$.

Step2: Read function values from the graph

From the graph, when $x = 5$, $f(5)=-5$; when $x = 7$, $f(7)=-5$.

Step3: Calculate the average rate of change

Substitute $f(5)=-5$, $f(7)=-5$, $a = 5$, and $b = 7$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{-5-(-5)}{7 - 5}=\frac{-5 + 5}{2}=\frac{0}{2}=0$.

Answer:

$0$