Algebraic functions

An algebraic function is a function $y=f(x)$ which satisfies a polynomial equation $p(x,y)=0$.

Alternatively, $a_{n}(x)y^{n}+a_{n-1}(x)y^{n-1}+a_{1}(x)y+a_{0}(x)=0$, where $a_{n}(x),a_{n-1}(x),\cdots ,a_{1}(x),a_{0}(x)$ are themselves polynomials in x.

A function which is not algebraic is called a transcendental function.