Polynomial functions are functions that can be expressed as the sum of terms involving powers of variables. The general form of a polynomial function is f(x) = a0 + a1x + a2x^2 + ... + anx^n, where the exponents n are non-negative integers and the coefficients a0, a1, ..., an are constants. Polynomial functions include linear, quadratic, and cubic functions as special cases where n is 1, 2, or 3.