Final answer:
Option A, P(x)=2x³+3x²-4x+4, is the polynomial function, as it consists of terms that have non-negative integer exponents and does not include division by a variable or fractional exponents. Therefore, the correct answer is option A. P(x)=2x³+3x²-4x+4.
Step-by-step explanation:
The question asks which of the given functions is a polynomial function. A polynomial function is an expression consisting of variables and coefficients that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Option A, P(x)=2x³+3x²-4x+4, is a polynomial because it is formed of a finite number of terms with non-negative integer powers of x and coefficients. Options B, C, and D are not polynomial functions because they contain negative exponents (B), division by a variable (C), and fractional exponents (D), which are not permitted in polynomial functions. Therefore, the answer is Option A.