Rational Functions. A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least 1. In other words, there must be a variable in the denominator. Examples: The parent function of a rational function is and the graph is a hyperbola.The domain and range is the set of all real numbers except 0. Excluded value. In a rational function, an excluded value is any x-value that makes the function value y undefined.ational Functions. A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least 1. In other words, there must be a variable in the denominator. Examples: The parent function of a rational function is and the graph is a hyperbola.