# How do you determine whether the function is a polynomial function f(x) = 2 - 2/x^6?

Feb 27, 2018

$\text{the function:" \quad f(x) \ = \ 2 - 2/x^6, \quad "is not a polynomial function.}$

$\text{Please see argument below.}$

#### Explanation:

$\text{We are given:} \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad f \left(x\right) \setminus = \setminus 2 - \frac{2}{x} ^ 6.$

$\text{One way of deciding if this function is a polynomial function is}$
$\text{the following:}$

$\text{1) We observe that this function," \ f(x), "is undefined at} \setminus x = 0.$

$\text{2) However, we recall that polynomial functions are, certainly,}$
$\setminus q \quad \setminus q \quad \text{defined everywhere.}$

$\text{So" \ f(x) \ "cannot be a polynomial function.}$

$\text{Hence, we conclude immediately:}$

$\text{the function:" \quad f(x) \ = \ 2 - 2/x^6, \quad "is not a polynomial function.}$