given the table: x f(x) -3 -2 -2 -3 -1 -2 0 1 what is the average rate of change between x = -2 and x = 0? 1…

Explanation:

Step1: Recall the average - rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$, $b = 0$.

Step2: Find $f(a)$ and $f(b)$ from the table

From the table, when $x=-2$, $f(-2)=-3$ (so $f(a)=-3$), and when $x = 0$, $f(0)=1$ (so $f(b)=1$).

Step3: Substitute values into the formula

Substitute $a=-2$, $b = 0$, $f(a)=-3$, and $f(b)=1$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(0)-f(-2)}{0-(-2)}=\frac{1-(-3)}{0 + 2}$.

Step4: Simplify the expression

First, simplify the numerator: $1-(-3)=1 + 3=4$. Then, the denominator is $0+2 = 2$. So, $\frac{4}{2}=2$.

Answer:

2