Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $2 \leq x \leq 8$.

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $f(x)$ over $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Identify values from the table

For $a=2$, $f(a)=42$; for $b=8$, $f(b)=6$.

Step3: Substitute values into formula

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

Step4: Calculate numerator and denominator

$\frac{-36}{6}$

Step5: Simplify the fraction

$-6$

Answer:

$-6$