Breuksfuncties

Breuksfuncties is the plural form of the term commonly used in Dutch for what is typically called rational functions in English. A breukfunctie, or rational function, is a function of a real variable x that can be written as a ratio of two polynomials: f(x) = P(x)/Q(x), where P and Q are polynomials and Q is not the zero polynomial. If P and Q share a common factor, the function can be simplified, but the original expression may have holes at the zeros of the common factor.

The domain of a breukfunctie consists of all real numbers for which the denominator Q(x) is not zero. The graph usually features vertical asymptotes at real zeros of Q and may have horizontal or oblique asymptotes determined by the degrees of P and Q: if deg P < deg Q, y = 0 is a horizontal asymptote; if deg P = deg Q, the horizontal asymptote is the ratio of leading coefficients; if deg P > deg Q, an oblique or higher-degree asymptote may occur.

Zeros of the function are the real roots of P that are not canceled by Q. Removable discontinuities occur at points where P and Q share a common factor that is canceled in simplified form.

Breukfuncties are closed under standard arithmetic operations and can be decomposed into partial fractions after factoring Q. This decomposition aids integration and certain analyses in algebra and calculus. In Dutch, “breukfunctie” or “breukfunctie” are the standard terms; “breuksfuncties” can appear as a misspelling or informal variant.