the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$ and $b=9$.

Step2: Estimate $f(2)$ and $f(9)$ from the graph

From the graph, when $x = 2$, $f(2)\approx - 10$. When $x = 9$, $f(9)\approx40$.

Step3: Calculate the average rate of change

Substitute $a = 2$, $b = 9$, $f(2)\approx - 10$ and $f(9)\approx40$ into the formula: $\frac{f(9)-f(2)}{9 - 2}=\frac{40-(-10)}{7}=\frac{40 + 10}{7}=\frac{50}{7}\approx7.14$.

Answer:

$\frac{50}{7}$