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 6 ≤ x ≤ 18. x f(x) 6 49 12 39 18 29 24 19 30 9

question given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 6 ≤ x ≤ 18. x f(x) 6 49 12 39 18 29 24 19 30 9

Answer

Answer:

$-\frac{5}{6}$

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, $a = 6$, $b = 18$, $f(6)=49$, and $f(18)=29$.

Step2: Substitute values into formula

$\frac{f(18)-f(6)}{18 - 6}=\frac{29 - 49}{18 - 6}$

Step3: Simplify the numerator and denominator

The numerator $29-49=-20$, and the denominator $18 - 6 = 12$. So we have $\frac{-20}{12}$.

Step4: Reduce the fraction

$\frac{-20\div4}{12\div4}=-\frac{5}{6}$