Question

question. given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 4 ≤ x ≤ 6.

x	3	4	5	6	7
f(x)	3	9	27	81	243

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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$, $b = 6$, $f(4)=9$, and $f(6)=81$.

Step2: Substitute values into formula

$\frac{f(6)-f(4)}{6 - 4}=\frac{81 - 9}{2}$.

Step3: Simplify the expression

$\frac{72}{2}=36$.

Answer:

$36$