# Polynomial Function

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

A polynomial function of degree $n$ is written as $f\left(x\right)={a}_{n}{x}^{n}+{a}_{n-1}{x}^{n-1}+{a}_{n-2}{x}^{n-2}+\cdots +{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}$ .

Polynomial functions are defined and continuous on all real numbers.

POLYNOMIALS OF LOW DEGREE
NAME FORM DEGREE
Constant Function
$f\left(x\right)=a$
$0$
Linear Function
$f\left(x\right)=ax+b,\text{\hspace{0.17em}}\text{\hspace{0.17em}}a\ne 0$
$1$
$f\left(x\right)=a{x}^{2}+bx+c,\text{\hspace{0.17em}}\text{\hspace{0.17em}}a\ne 0$
$2$
$f\left(x\right)=a{x}^{3}+b{x}^{2}+cx+d,\text{\hspace{0.17em}}\text{\hspace{0.17em}}a\ne 0$
$3$
$f\left(x\right)=a{x}^{4}+b{x}^{3}+c{x}^{2}+dx+e,\text{\hspace{0.17em}}\text{\hspace{0.17em}}a\ne 0$
$4$