Final answer:
Answer A, P(x) = 2x + 3x - 4x + 4, is the correct choice because it is the only function among the options given that satisfies the criteria of a polynomial function with variables to whole number exponents and no variables in the denominator.
Step-by-step explanation:
The question asks which of the given options is a polynomial function. A polynomial function is an expression consisting of variables and coefficients, with only whole number exponents and no variables in the denominator. Now let's analyze the options:
• A. P(x) = 2x + 3x - 4x + 4 - This is a polynomial because it consists of terms with variables to whole number exponents and has no denominators with variables.
• B. H(x) = 4x¹/² + 3x -4 - This is not a polynomial since the exponent 1/2 is not a whole number.
• C. G(x) = 2x⁻³ + 5 - This is not a polynomial because the exponent -3 is a negative whole number, making it a reciprocal of x, which is not allowed in a polynomial.
• D. F(x) = 2x³ - 5x + 3 / 3x² - This is not a polynomial because there is a variable in the denominator.
Therefore, the correct answer is A. P(x) = 2x + 3x - 4x + 4 because it is the only function that satisfies all criteria for a polynomial function.