What characterizes a polynomial function?

A polynomial function is characterized by its structure, which involves constants, variables, and exponents combined through basic operations such as addition, subtraction, and multiplication. This means a polynomial can consist of one or more terms, where each term is made up of a coefficient (constant) multiplied by the variable raised to a non-negative integer exponent. The key aspects are that the exponent of the variable must be a whole number, and the coefficients must be real numbers.

The definition of a polynomial embraces a wide range of functions, from simple linear functions (like (2x + 3)) to more complex forms (like (x^3 - 4x + 7)). This versatility allows for polynomial functions of varying degrees, and they are not restricted to single-variable equations; a polynomial can indeed have multiple variables (e.g., (x^2 + y^2)).

By contrast, the other options do not accurately capture the essence of polynomial functions. The requirement for them to be a single variable with exponents is too limiting, and not all polynomial functions are quadratic; they can range from linear to cubic and beyond. The stipulation that they only contain real numbers is also incorrect since polynomials can include complex coefficients too, though