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 ≤ 3?

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, $a=-7$ and $b = 3$.

Step2: Find $f(-7)$ and $f(3)$ from the graph

From the graph, when $x=-7$, $f(-7)=-80$. When $x = 3$, $f(3)=20$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(3)-f(-7)}{3-(-7)}=\frac{20-(-80)}{3 + 7}=\frac{20 + 80}{10}=\frac{100}{10}=10$.

Answer:

$10$