Question

1. find the average rate of change for the function, shown above, over the interval -3 ≤ x ≤ -1.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-3$, $b = - 1$.

Step2: Identify function values from the graph

From the graph, when $x=-3$, assume the point is $(-3,y_1)$ and when $x=-1$, assume the point is $(-1,y_2)$. Let's say $f(-3)=y_1$ and $f(-1)=y_2$. We need to find the $y$ - values corresponding to $x=-3$ and $x = - 1$ from the graph. Suppose $f(-3)=2$ and $f(-1)=-1$.

Step3: Calculate the average rate of change

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

Answer:

$-\frac{3}{2}$