An algebraic function is a type of function defined as the root of a polynomial equation with coefficients in the real or complex numbers. It can be expressed using a finite number of operations involving addition, subtraction, multiplication, division, and taking roots.
Polynomial Function: A special class of algebraic functions characterized by expressions involving only non-negative integer powers of x.
Rational Function: A ratio of two polynomial functions where the denominator is not zero.
Root Function: $f(x) = x^{1/n}$ where $n$ is a positive integer. These are also considered algebraic functions.