Väärtusvahemik

väärtusvahemik, often translated as value range or scope of values, refers to the set of all possible values that a variable, function, or expression can take. In mathematics, this concept is fundamental and appears in various contexts. For instance, the väärtusvahemik of a function is the set of all output values it can produce. This is distinct from the domain, which is the set of all possible input values.

Understanding the väärtusvahemik is crucial for analyzing the behavior of mathematical objects. For a real-valued function f, its väärtusvahemik is denoted by Im(f) or R(f) and consists of all y such that y = f(x) for some x in the domain of f. For example, the function f(x) = x^2 has a väärtusvahemik of [0, ∞) because the square of any real number is non-negative.

In statistics, the term can refer to the range of values within a dataset, often calculated as the difference between the maximum and minimum values. This provides a simple measure of dispersion. In programming, a variable might have a defined väärtusvahemik, such as integer types having a specific range of representable numbers. The concept helps in predicting outcomes, defining constraints, and ensuring the correctness of calculations. When discussing inequalities, the väärtusvahemik represents all numbers that satisfy the given condition.