h(x) = -7x

Question

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

Answer 1

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 1-3 terms are excluded from the definition.

Answer 2

why would something like y=x^-3 not be a polynomial function?

Answer 3

must the value of n always be nonnegetive?

Answer 4

Yes, the exponents have to be non-negative (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 non-negative whole number exponents."

Answer 5

and for something like
y=cosx

that dosent work cause cos is not a real number?

Answer 6

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.

Answer 7

Thank you :D

Answer 8

You're welcomd!