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

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 attempt 2 out of 2

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 attempt 2 out of 2

Answer

Answer:

$-\frac{5}{6}$

Explanation:

Step1: Recall the formula

The average - rate - of - change formula 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

Substitute into the formula: $\frac{f(18)-f(6)}{18 - 6}=\frac{29 - 49}{18 - 6}$.

Step3: Calculate numerator and denominator

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

Step4: Simplify the fraction

Simplify $\frac{-20}{12}$ by dividing both the numerator and denominator by their greatest common divisor, which is 4. $\frac{-20\div4}{12\div4}=-\frac{5}{6}$.