Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -5 ≤ x ≤ -2?

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-5$ and $b = - 2$.

Step2: Determine $f(-5)$ and $f(-2)$ from the graph

From the graph, when $x=-5$, $f(-5)=-8$; when $x = - 2$, $f(-2)=-4$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(-2)-f(-5)}{-2-(-5)}=\frac{-4-(-8)}{-2 + 5}=\frac{-4 + 8}{3}=\frac{4}{3}$.

Answer:

$\frac{4}{3}$