Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -2 ≤ 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, $a=-2$ and $b = 3$.

Step2: Find $f(-2)$ and $f(3)$ from the graph

From the graph, when $x=-2$, $y = f(-2)=0$. When $x = 3$, $y=f(3)=30$.

Step3: Calculate the average rate of change

Substitute $f(-2)=0$, $f(3)=30$, $a=-2$, and $b = 3$ into the formula: $\frac{f(3)-f(-2)}{3-(-2)}=\frac{30 - 0}{3+2}=\frac{30}{5}=6$.

Answer:

6