consider the graph of f(x). what is the average rate of change of f(x) from x1 = 4 to x2 = 7? please write…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x_1$ to $x_2$ is given by $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.

Step2: Identify $x_1$, $x_2$, $f(x_1)$ and $f(x_2)$

From the graph, when $x_1 = 4$, $f(x_1)=13$; when $x_2 = 7$, $f(x_2)=11$.

Step3: Substitute values into formula

$\frac{f(7)-f(4)}{7 - 4}=\frac{11 - 13}{3}$.

Step4: Simplify the fraction

$\frac{11 - 13}{3}=\frac{-2}{3}=-\frac{2}{3}$.

Answer:

$-\frac{2}{3}$