A rational function is a function that is the ratio of two polynomial functions, where the denominator polynomial is not equal to zero. It can be represented as R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions such that Q(x) ≠ 0. The domain of a rational function is the set of all values of x for which the denominator is not zero. Some key features of rational functions include:

• Degree: The degree of a rational function is the maximum of the degrees of its constituent polynomials P and Q, when the fraction is reduced to lowest terms. If the degree of the rational function is d, then the equation is of the form P(x)/Q(x), where P(x) and Q(x) are polynomials of degree n and m, respectively, and d = n - m.

• Asymptotes: An asymptote is a line or curve that the graph of the function approaches but never touches. Rational functions can have three types of asymptotes: horizontal, vertical, and oblique. The vertical asymptotes occur at the zeros of the denominator polynomial, while the horizontal asymptotes occur at the ratio of the leading coefficients of the numerator and denominator polynomials. Oblique asymptotes occur when the degree of the numerator polynomial is exactly one greater than the degree of the denominator polynomial.

Rational functions are used to model more complex equations in science and engineering, including fields and forces in physics, spectroscopy in analytical chemistry, enzyme kinetics in biochemistry, electronic circuitry, aerodynamics, medicine concentrations in vivo, wave functions for atoms and molecules, and more.