Question

Match the average rates of change of f(x) with the corresponding intervals.

Answer 1

The average rate change of a function is given by the formula: $AG= \frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1} }$
So lets apply our formula to each one of our intervals:

For [-4,-2]
$AV= \frac{-12-0}{-4-(-2)} =6$

For [-2,1]
$AV= \frac{0-3}{-2-1} =1$

For [-3,1]
$AV= \frac{-5-3}{-3-1} =2$

For [-4,0]
$AV= \frac{-12-4}{-4-0}=4$

We can conclude that you should fill your table as follows:
[-4,-2]----->6

[-2,1]----->1

[-3,1]----->2

[-4,0]----->4