Final answer:
Option A, P(x) = 2x³ + 3x² - 4x + 4, is the correct answer as it is a polynomial function with terms that have non-negative integer exponents.
Step-by-step explanation:
The student has asked which of the provided options is a polynomial function. A polynomial function is a function that is composed of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
Now let's examine the options given:
- A. P(x) = 2x³ + 3x² - 4x + 4 - This is a polynomial function because it has terms with non-negative integer exponents and consists of the operations mentioned.
- B. G(x) = 2x⁻³+5 - This is not a polynomial function because it contains a negative exponent.
- C. H (X) = 4x¹⁄₂ + 3x -4 - This is not a polynomial function because it contains a fractional exponent.
- D. F f = 2x³ - 5x + 3/3x² - This is not a polynomial function because it involves division by a variable expression.
Therefore, the correct answer is A. P(x) = 2x³ + 3x² - 4x + 4, which is indeed a polynomial function.