Polynomial functions

A polynomial function is a function defined by evaluating a polynomial. A function ƒ of one argument is called a polynomial function if it satisfies

ƒ(x) = anxn + an−1xn−1 + ... + a2x2 + a1x + a0

for all arguments x, where n is a nonnegative integer and a0, a1,a2, ..., an are constant coefficients.
For example, the function f, taking real numbers to real numbers, defined by

is a polynomial function of one argument. Polynomial functions of multiple arguments can also be defined, using polynomials in multiple variables, as in

Polynomial functions are an important class of smooth functions.