What is a polynomial function?

1 Answer
Sep 13, 2014

A polynomial function in standard form must look like:

f(x)=a_nx^n+a_(n-1)x^(n-1)+a_(n-2)x^(n-2)+...+a_2x^2+a_1x+a_0

where n in NN and a_i in ZZ, i in {0, 1, 2, ..., n}

If you are not familiar with the notation, NN is the set of natural number, and ZZ is the set of integers.

Examples of polynomial functions in standard form:

f(x)=-4x^5+7x^3-6x^2+4
g(x)=3x^4-4x^3+6x-9

Examples of non polynomial functions:

h(x)=4x^7-3x^5+sqrt(2x)-5
j(x)=-7x^3-2x^2+5/(x^3)
k(x)=4.5x^5-3x^2

I'll leave it to you to figure out why they are non polynomial functions.