Algebraic functions

An algebraic function is a function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = f(x)} which satisfies a polynomial equation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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.