Final answer:
The function f(x) = x^(3/2) - 7x + 3 is not a polynomial because it contains a term with a fractional exponent, which does not meet the definition of a polynomial with non-negative integer exponents.
Step-by-step explanation:
The student asks whether the function f(x) = x(3/2) - 7x + 3 is a polynomial. By definition, a polynomial is an expression consisting of variables and coefficients that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. The term x(3/2) indicates a square root, which is not a non-negative integer exponent. Consequently, f(x) is not a polynomial because it includes a fractional exponent.