Question 1086959
Question:
Determine whether the function is a polynomial function.
f(x) = x^3/2 - x^6 + 6
 
Solution:
This question shows the importance of the PEMDAS rules, and why we should stick to the rules.
 
A polynomial is an expression of *one or more* algebraic terms, especially the sum of several terms that contain different *non-negative integrer* powers of the same variable(s).
(above definition is adapted from Google definition, which defines poly in the usual sense of two or more.  In math, a monomial is also considered a polynomial for generality, also, the important condition of *non-negative integer* powers was added).

As it is, the rules of PEMDAS interpret the function as:
f(x) = (x³)/2 - x^6 +6    [exponential before multiplication/division]
which makes it a polynomial, because the powers are non-negative integer powers.
 
However, I have a hunch that the question was meant to read
f(x) = x<sup>3/2</sup> - x^6 +6
which makes it a non-integer power, and therefore this second case is not a polynomial.  The answer can only be determined after confirmation of the question.