9 what is the average rate of change over the interval -4 ≤ x ≤ -1? x f(x) -4 -8 -2 0 0 -2 -1 1 a 0 b 16/6 c…

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, $a=-4$ and $b = - 1$. We need to find $f(-4)$ and $f(-1)$. From the table, when $x=-4$, assume $f(-4)=-8$ (the value corresponding to $x = - 4$ in the table), and when $x=-1$, $f(-1)=1$.

Step2: Calculate the average rate of change

Substitute $a=-4$, $b=-1$, $f(-4)=-8$ and $f(-1)=1$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(-1)-f(-4)}{-1-(-4)}=\frac{1-(-8)}{-1 + 4}=\frac{1 + 8}{3}=\frac{9}{3}=3$.

Answer:

C. 3