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 3 ≤ x ≤ 15. x f(x) 0 19 3 22 6 25 9 28 12 31 15 34 answer attempt 1 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 3 ≤ x ≤ 15. x f(x) 0 19 3 22 6 25 9 28 12 31 15 34 answer attempt 1 out of 2

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, $a = 3$ and $b = 15$.

Step2: Find $f(3)$ and $f(15)$ from the table

From the table, when $x = 3$, $f(3)=22$; when $x = 15$, $f(15)=34$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(15)-f(3)}{15 - 3}=\frac{34 - 22}{12}=\frac{12}{12}=1$.

Answer:

$1$