question given the function defined in the table below, find the average rate of change, in simplest form…

question given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 18 ≤ x ≤ 36. x f(x) 0 13 9 25 18 37 27 49 36 61

question given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 18 ≤ x ≤ 36. x f(x) 0 13 9 25 18 37 27 49 36 61

Answer

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, $a = 18$, $b = 36$, $f(a)=f(18) = 37$, and $f(b)=f(36)=61$.

Step2: Substitute values into formula

$\frac{f(36)-f(18)}{36 - 18}=\frac{61 - 37}{36 - 18}$.

Step3: Simplify the expression

First, calculate the numerator: $61-37 = 24$. Then, calculate the denominator: $36 - 18=18$. So, $\frac{24}{18}=\frac{4}{3}$.

Answer:

$\frac{4}{3}$