Rational functions are mathematical expressions that represent the ratio of two polynomials. They can be written in the form f(x) = P(x) / Q(x), where P(x) and Q(x) are polynomials. These functions are defined for all values of x except where the denominator Q(x) equals zero, which creates vertical asymptotes in their graphs. The behavior of rational functions can be analyzed using concepts such as asymptotes, intercepts, and end behavior. They are essential in various fields, including engineering and economics, as they model real-world situations where relationships between quantities are expressed as ratios.