Final answer:
The function -6x^2 - 12x + 1 is a polynomial function because it comprises a sum of powers of x with whole number exponents and coefficients. It is not a single-term power function; therefore, the correct category is b. Polynomial function.
Step-by-step explanation:
The function -6x^2 - 12x + 1 is considered a polynomial function because it is a sum of powers of x with non-negative integer exponents and a combination of real number coefficients.
On the other hand, a power function is of the form f(x) = k*x^n where k is a constant, and n is a real number. The given function does not fit this form due to the presence of multiple terms with different exponents.
Based on these considerations, the function belongs to category b. Polynomial function.