The simplest type of functions are polynomial ones. They are easy to evaluate their derivatives, integrals, zeroes and basically most notions you can associate to a function. Furthermore polynomial functions can be used to suitably approximate any other function in a specific interval by the Stone_Weierstrass Theorem. It is also quite easy to approximate suitable datasets by regression methods provided you use a high enough degree polynomial but not large enough to cause "overfitting". Now to find what degree you need there are a couple of methods, the easiest being just to conduct a visual inspection and note how many monotonicity changes you get. Notice that linear regression (if you are familiar with the term) is just a simple case of polynomial regression.

Dear Markos Karameris, thanks!