In order to determine the average rate of change, use the following formula:
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are two points of the curve.
For x=1 and x=3 you have:
(x1,y1) = (1,2)
(x2,y2) = (3,3)
replace the previous values of the coordinates into the expression for m:
m = (3-2)/(3-1)
m = 1/2
Hence, the rate of change is 1/2