Question

What is a polynomial function?

Answer 1

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.