Question

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

Answer 1

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

`"Please see argument below."`

Explanation:

`"We are given:" \qquad \qquad \qquad \qquad f(x) \ = \ 2 - 2/x^6.`

`"One way of deciding if this function is a polynomial function is"`
`"the following:"`

`"1) We observe that this function," \ f(x), "is undefined at" \ x=0.`

`"2) However, we recall that polynomial functions are, certainly,"`
`\qquad \qquad "defined everywhere."`

`"So" \ f(x) \ "cannot be a polynomial function."`

`"Hence, we conclude immediately:"`

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