Math:Polynomial Functions
posted by Lena on .
h(x) = 7x
I was thinking that this was not a polynomial function because 7x is just one term making it a monomial but the answer key says it is a polynomial function. Could someone explain why that is so? Thanks :D

You have a point, but the definitions are that
a monomial has only one term,
a binomial has exactly two terms,
a trinomial has exactly three terms, and
a polynomial has at least one term.
Ususally polynomial is used when the number of terms is numerous, unknown or indefinite. It would be too restrictive if 13 terms are excluded from the definition. 
why would something like y=x^3 not be a polynomial function?

must the value of n always be nonnegetive?

Yes, the exponents have to be nonnegative (i.e. zero allowed, thus constant terms) and integers. x^{2/3} and x^{2} are not polynomials.
The definition of a polynomial, as per Wiki, is as follows:
"In mathematics, a polynomial is a finite length expression constructed from variables (also known as indeterminates) and constants, by using the operations of addition, subtraction, multiplication, and constant nonnegative whole number exponents." 
and for something like
y=cosx
that dosent work cause cos is not a real number? 
That works, but as a trigonometric function and not a polynomial function. I the definition of a polynomial function, the right hand side must be a polynomial, as defined above.

Thank you :D

You're welcomd!