a function of x is shown on the graph. which is the best estimate of the average rate of change of 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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$, $b = 2$.

Step2: Estimate $f(-2)$ and $f(2)$ from the graph

From the graph, when $x=-2$, $f(-2)\approx0$. When $x = 2$, $f(2)\approx8$.

Step3: Calculate the average rate of change

Substitute $a=-2$, $b = 2$, $f(-2)\approx0$, and $f(2)\approx8$ into the formula: $\frac{f(2)-f(-2)}{2-(-2)}=\frac{8 - 0}{4}=\frac{8}{4}=2$. The closest value to 2 among the options is C. 1.9375.

Answer:

C. 1.9375