A rational function is a type of 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. Rational functions are defined for all real numbers except where the denominator Q(x) equals zero, which creates vertical asymptotes in their graphs. These functions can exhibit various behaviors, including horizontal and vertical asymptotes, and can be used to model real-world situations. Understanding rational functions is essential in algebra and calculus, as they play a significant role in analyzing limits and continuity.