Polynomial Function

A polynomial function is a function in which $f (x)$ is a polynomial in $x$ .

A polynomial function of degree $n$ is written as $f (x) = a_{n} x^{n} + a_{n - 1} x^{n - 1} + a_{n - 2} x^{n - 2} + \dots + a_{2} x^{2} + a_{1} x + a_{0}$ .

Polynomial functions are defined and continuous on all real numbers.

POLYNOMIALS OF LOW DEGREE
NAME	FORM	DEGREE
Constant Function	$f (x) = a$	$0$
Linear Function	$f (x) = a x + b, a \neq 0$	$1$
Quadratic Function	$f (x) = a x^{2} + b x + c, a \neq 0$	$2$
Cubic Function	$f (x) = a x^{3} + b x^{2} + c x + d, a \neq 0$	$3$
Quartic Function	$f (x) = a x^{4} + b x^{3} + c x^{2} + d x + e, a \neq 0$	$4$

Polynomial Function

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