Question

using the graph below find the average rate of change on -1,2.

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, $a=-1$ and $b = 2$.

Step2: Find $f(-1)$ and $f(2)$ from the graph

From the graph, when $x=-1$, $y = 0$, so $f(-1)=0$. When $x = 2$, $y=-3$, so $f(2)=-3$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(2)-f(-1)}{2-(-1)}=\frac{-3 - 0}{2 + 1}=\frac{-3}{3}=-1$.

Answer:

$-1$