a function is graphed below. on which interval of x is the average rate of change of the function the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.

Step2: Calculate average rate of change for $[1,5]$

Let $x_1 = 1$, $y_1=7$, $x_2 = 5$, $y_2 = 18$. Then $\frac{y_2 - y_1}{x_2 - x_1}=\frac{18 - 7}{5 - 1}=\frac{11}{4}=2.75$.

Step3: Calculate average rate of change for $[5,8]$

Let $x_1 = 5$, $y_1 = 18$, $x_2 = 8$, $y_2 = 25$. Then $\frac{y_2 - y_1}{x_2 - x_1}=\frac{25 - 18}{8 - 5}=\frac{7}{3}\approx2.33$.

Step4: Calculate average rate of change for $[8,16]$

Let $x_1 = 8$, $y_1 = 25$, $x_2 = 16$, $y_2 = 33$. Then $\frac{y_2 - y_1}{x_2 - x_1}=\frac{33 - 25}{16 - 8}=\frac{8}{8}=1$.

Step5: Calculate average rate of change for $[16,22]$

Let $x_1 = 16$, $y_1 = 33$, $x_2 = 22$, $y_2 = 47$. Then $\frac{y_2 - y_1}{x_2 - x_1}=\frac{47 - 33}{22 - 16}=\frac{14}{6}=\frac{7}{3}\approx2.33$.

Answer:

$[8,16]$