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= (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= (-12-0)/(-4-(-2)) =6`

For [-2,1]

`AV= (0-3)/(-2-1) =1`

For [-3,1]

`AV= (-5-3)/(-3-1) =2`

For [-4,0]

`AV= (-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