Solution:
I think I have seen this question elsewhere today. :)
Assuming no missing parentheses, ie. properly interpreted using PEMDAS rules,
f(x) = (x^3)/2 - x^6 + 6
the function has one or more terms, each of which has a variable (or more) raised to a non-negative integer power. Therefore the function is a polynomial.
A detailed definition and explanation of a polynomial, and the related terms, can be found :
https://en.wikipedia.org/wiki/Polynomial