Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -7 ≤ 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, $a=-7$ and $b = 2$.

Step2: Estimate function values from graph

From the graph, estimate $f(-7)\approx - 20$ and $f(2)\approx - 25$.

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(2)-f(-7)}{2-(-7)}=\frac{-25 - (-20)}{2 + 7}=\frac{-25 + 20}{9}=\frac{-5}{9}=-\frac{5}{9}$.

Answer:

$-\frac{5}{9}$