Ortswert

Ortswert is the value of a function at a point. If f is defined on a domain containing x0, then the Ortswert of f at x0 is f(x0). Geometrically, this is the y-coordinate of the point (x0, f(x0)) on the graph of f.

In modern German mathematics, the standard term is Funktionswert; Ortswert is largely historical or regional and may be found in older texts or informal explanations.

Examples help illustrate the concept. For f(x) = x^2, the Ortswert at x0 = 3 is f(3) = 9. For f(x) = sin x, at x0 = π/2, the Ortswert is 1. The Ortswert is a single value determined by the input x0 and the given function.

As with any function value, the Ortswert depends on the function’s domain and on the input x0. In the graph of f, the Ortswert corresponds to the point’s ordinate (the y-coordinate). The collection of all Ortswerte as x0 varies over the domain is the function’s range. In contemporary usage, the term Funktionswert is preferred, while Ortswert may appear in historical contexts or didactic materials.