the table shows the values of a function f(x). what is the average rate of change of f(x) from -2 to 2…

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$, $b = 2$, $f(-2)=25$, and $f(2)=9$.

Step2: Substitute values into formula

$\frac{f(2)-f(-2)}{2-(-2)}=\frac{9 - 25}{2+2}$.

Step3: Simplify the expression

$\frac{9 - 25}{2 + 2}=\frac{-16}{4}=-4$.

Answer:

$-4$