Question

find the average rate of change of the function below on the interval -3,2. round to 2 decimal places, if necessary.

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, $a=-3$, $b = 2$. We need to find the function values at $x=-3$ and $x = 2$. From the graph, when $x=-2,y = 1$ and when $x = 3,y=-0.25$. We assume the function is defined such that we can use the two - point formula for the average rate of change on the interval $[-3,2]$. Let $(x_1,y_1)$ and $(x_2,y_2)$ be two points on the function. The average rate of change formula is $\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Identify the points

Let's assume we can use the points $(-2,1)$ and $(3,-0.25)$ to approximate the average rate of change on $[-3,2]$. Here, $x_1=-2,y_1 = 1,x_2 = 3,y_2=-0.25$.

Step3: Calculate the average rate of change

Substitute the values into the formula: $\frac{y_2 - y_1}{x_2 - x_1}=\frac{-0.25 - 1}{3-(-2)}=\frac{-1.25}{5}=-0.25$.

Answer:

$-0.25$