A rational function is a type of mathematical function that can be expressed as the ratio of two polynomial functions. It is typically written in the form f(x) = P(x) / Q(x), where P(x) and Q(x) are polynomials. The domain of a rational function includes all real numbers except where the denominator Q(x) equals zero, as this would make the function undefined. Rational functions can exhibit various behaviors, such as asymptotes and intercepts. Vertical asymptotes occur at the values of x that make Q(x) = 0, while horizontal asymptotes describe the behavior of the function as x approaches infinity. Understanding these characteristics helps in graphing and analyzing rational functions.