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

The average rate change of a function is given by the formula: 
So lets apply our formula to each one of our intervals:

For [-4,-2]


For [-2,1]


For [-3,1]


For [-4,0]


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

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

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

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