What is a polynomial function?

Question

4102 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-09-13T04:51:01

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.