The average rate change of a function is given by the formula: [tex]AG= \frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1} } [/tex]
So lets apply our formula to each one of our intervals:
For [-4,-2]
[tex]AV= \frac{-12-0}{-4-(-2)} =6[/tex]
For [-2,1]
[tex]AV= \frac{0-3}{-2-1} =1[/tex]
For [-3,1]
[tex]AV= \frac{-5-3}{-3-1} =2[/tex]
For [-4,0]
[tex]AV= \frac{-12-4}{-4-0}=4 [/tex]
We can conclude that you should fill your table as follows:
[-4,-2]----->6
[-2,1]----->1
[-3,1]----->2
[-4,0]----->4
