A rational function is a function that can be written as the ratio of two polynomial functions. The general form is f(x) = P(x) / Q(x), where P(x) and Q(x) are polynomials and Q(x) is not the zero polynomial. The domain of a rational function excludes any values of x for which Q(x) = 0, as division by zero is undefined. Vertical asymptotes often occur at these excluded x-values. Horizontal asymptotes describe the behavior of the function as x approaches positive or negative infinity, and their existence depends on the degrees of P(x) and Q(x).