5 mark for review the graph of the function f, shown above, consists of three line segments. what is the…

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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$ and $b = 6$.

Step2: Find $f(-1)$ and $f(6)$ from the graph

From the graph, when $x=-1$, $y = f(-1)=0$; when $x = 6$, $y=f(6)=0$.

Step3: Calculate the average rate of change

Substitute $f(-1)=0$, $f(6)=0$, $a=-1$, and $b = 6$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{0 - 0}{6-(-1)}=\frac{0}{7}=0$.

Answer:

B. 0