a function is graphed below. on which interval of x is the average rate of change of t\nanswer\nx = 2 to x =…

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 rate for $x = 2$ to $x = 12$

Let $a = 2$, $b = 12$, $f(2)=7$, $f(12)=13$. Then $\frac{f(12)-f(2)}{12 - 2}=\frac{13 - 7}{10}=\frac{6}{10}=0.6$.

Step3: Calculate rate for $x = 12$ to $x = 23$

Let $a = 12$, $b = 23$, $f(12)=13$, $f(23)=30$. Then $\frac{f(23)-f(12)}{23 - 12}=\frac{30 - 13}{11}=\frac{17}{11}\approx1.55$.

Step4: Calculate rate for $x = 23$ to $x = 48$

Let $a = 23$, $b = 48$, $f(23)=30$, $f(48)=39$. Then $\frac{f(48)-f(23)}{48 - 23}=\frac{39 - 30}{25}=\frac{9}{25}=0.36$.

Step5: Calculate rate for $x = 48$ to $x = 77$

Let $a = 48$, $b = 77$, $f(48)=39$, $f(77)=57$. Then $\frac{f(77)-f(48)}{77 - 48}=\frac{57 - 39}{29}=\frac{18}{29}\approx0.62$.

Answer:

$x = 12$ to $x = 23$