Linear function, quadratic function, cubic function, exponential function, logarithmic function, power function, trigonometric function and double hook function (e.g. y = ax+b/x (a > 0, b>0)) The composite function is the synthesis of several different functions, and few others.

Periodic functions are often tested by abstract functions, and trigonometric functions are also periodic functions.

There are not many function types mainly because of application.