We are given the following function:
[tex]\frac{1}{xy^3}[/tex]We are asked to determine what type of function is.
An expression of the form:
[tex]ax^my^n\ldots z^l[/tex]This means a product of constant and variables elevated to different exponents is called a "monomial". If we have the sum of two monomials, like this:
[tex]a_1x^{m1}y^{n1}\ldots z^{l1}+a_2x^{m2}y^{n2}\ldots z^{l2}[/tex]Then, this is called a binomial.
If we have the sum of three monomials, like for example:
[tex]a_1x^{m1}y^{n1}\ldots z^{l1}+a_2x^{m2}y^{n2}\ldots z^{l2}+a_3x^{m3}y^{n3}\ldots z^{l3}[/tex]It is called a trinomial. And if we have more than 3 monomials then it is called a "polynomial".
The given function is the quotient between two functions, therefore, it is not any of the given types of functions.
The given function:
[tex]3x^2+5y^3[/tex]Here, we have two monomials:
[tex]\begin{gathered} 3x^2,\text{ and } \\ 5y^3 \end{gathered}[/tex]This means that the expression is a binomial.