egyváltozós

Egy évváltozós or egyeváltozós is a Hungarian mathematical term used to describe objects that depend on a single independent variable. The word combines egy/egyed and változó (variable) and is used to distinguish one-variable contexts from multivariable situations. In practice, egyeváltozós is commonly applied to functions, equations, and problems that involve only one variable.

In the context of functions, an egyváltozós fuggvény (often written as egyváltozós függvény) is a function from a subset of the real numbers to the real numbers, typically written as f(x). It describes a relation where the output depends on one input variable. Graphically, an egyváltozós függvény corresponds to a curve in the plane given by y = f(x). This is to be contrasted with többváltozós függvény, which depends on two or more variables (for example f(x, y)).

In the context of equations, egyváltozós egyenlet contain a single unknown. Examples include 3x + 2 = 7 or x^2 − 5x + 6 = 0. Solving such equations yields the values of the single variable that satisfy the statement.

In calculus and analysis, egyeváltozós problems involve functions of one variable, with techniques such as differentiation, integration, and single-variable optimization. Typical tasks include finding derivatives, locating extrema, or computing definite integrals with respect to the sole variable.

The term is contrasted with többváltozós, which describes objects depending on two or more variables. Orthographic variants exist in Hungarian, such as egyváltozós or egyeváltozós, depending on style and context.