Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -3 ≤ x ≤ 1?

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, $a=-3$ and $b = 1$.

Step2: Find $f(-3)$ and $f(1)$ from the graph

From the graph, when $x=-3$, $f(-3)=-30$. When $x = 1$, $f(1)=10$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(1)-f(-3)}{1-(-3)}=\frac{10-(-30)}{1 + 3}=\frac{10 + 30}{4}=\frac{40}{4}=10$.

Answer:

$10$