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 1-3 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 non-negative (i.e. zero allowed, thus constant terms) and integers. x2/3 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."
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!
Certainly! I'd be happy to explain why the function h(x) = -7x is considered a polynomial function.
In mathematics, a polynomial function is defined as a function that consists of one or more terms, where each term is a constant multiplied by one or more variables raised to non-negative integer exponents.
In this case, the function h(x) = -7x consists of a single term, -7x, where -7 is a constant and x is the variable raised to the first power.
Although it may seem like a monomial at first glance, it actually fits the definition of a polynomial. The reason is that a monomial is a specific type of polynomial with only one term. So, in this case, -7x can be considered as a monomial and a polynomial simultaneously.
It's important to note that polynomial functions can have multiple terms as well. For example, if we had h(x) = 3x^2 - 2x + 1, it would still be a polynomial function because it consists of three terms: 3x^2, -2x, and 1.
I hope this clarifies why h(x) = -7x is classified as a polynomial function!