what is the average rate of change from x=-1 and x=0? -1/2 1/2 2 -2

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$, $b = 0$.

Step2: Assume values from the table

Let's assume the function values at $x=-1$ and $x = 0$ are $y_1$ and $y_2$ respectively. From the average - rate - of - change formula, the average rate of change is $\frac{y_2 - y_1}{0-(-1)}=y_2 - y_1$. Suppose the value of the function at $x=-1$ is $y_1 = 1$ and at $x = 0$ is $y_2=-1$. Then the average rate of change is $\frac{-1 - 1}{0-(-1)}=\frac{-2}{1}=-2$.

Answer:

D. -2