Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -1 ≤ x ≤ 4?

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, $a=-1$ and $b = 4$.

Step2: Find $f(-1)$ and $f(4)$ from the graph

From the graph, when $x=-1$, $f(-1)=-20$. When $x = 4$, $f(4)=50$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(4)-f(-1)}{4-(-1)}=\frac{50-(-20)}{4 + 1}=\frac{50 + 20}{5}=\frac{70}{5}=14$.

Answer:

$14$