There are many types of functions, and the basic elementary functions are as follows:

Power function: y = x a

Exponential function: y = a x

Logarithmic function: y=loga x

Trigonometric function: y=sinx, etc

Inverse trigonometric function: y=arcsinx, etc.

Elementary function refers to the function formed by four operations and finite synthesis of basic elementary functions, such as quadratic function y = ax 2+bx+c and hyperbolic function y=sinhx.

As for other functions, it is more complicated.

For example, find the function y=[x] of the largest integer not greater than x, find the number y=φ(x) of numbers that are coprime with x and less than or equal to x, and so on.

There are also various piecewise functions that are not elementary functions.