Thread: What is the best model?

Ok so I am given this table ( or tables) of data and we have to create a model for it and it recommends a combination of functions so i decided to do a piecewise function. There are three tables, for the first one i decided to go with a cubic function, for the second one i went with a sine function but I don't know which function to go with for the last table. Can anyone please help determine the function/ model best for the data. And also for the other functions i let 1980= 0, 1981 = 1 and so on. I also have another question; how would i write the domain and range of this data (all of it) and what number set would it be?
thanks