given the function defined in the table below, find the average rate of the function over the interval 2 ≤ x…

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, $a = 2$, $b = 8$, $f(a)=f(2)=42$, and $f(b)=f(8)=6$.

Step2: Substitute values into formula

$\frac{f(8)-f(2)}{8 - 2}=\frac{6 - 42}{6}$.

Step3: Simplify the expression

$\frac{6-42}{6}=\frac{- 36}{6}=-6$.

Answer:

$-6$