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 $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Calculate average rate of change for $x = 0$ to $x = 1$

Given $(a,f(a))=(0,9)$ and $(b,f(b))=(1,18)$. Then $\frac{f(1)-f(0)}{1 - 0}=\frac{18 - 9}{1}=9$.

Step3: Calculate average rate of change for $x = 1$ to $x = 5$

Given $(a,f(a))=(1,18)$ and $(b,f(b))=(5,33)$. Then $\frac{f(5)-f(1)}{5 - 1}=\frac{33 - 18}{4}=\frac{15}{4}=3.75$.

Step4: Calculate average rate of change for $x = 5$ to $x = 9$

Given $(a,f(a))=(5,33)$ and $(b,f(b))=(9,50)$. Then $\frac{f(9)-f(5)}{9 - 5}=\frac{50 - 33}{4}=\frac{17}{4}=4.25$.

Step5: Calculate average rate of change for $x = 9$ to $x = 18$

Given $(a,f(a))=(9,50)$ and $(b,f(b))=(18,55)$. Then $\frac{f(18)-f(9)}{18 - 9}=\frac{55 - 50}{9}=\frac{5}{9}\approx0.56$.

Answer:

$x = 9$ to $x = 18$