Range

Range is a term used across disciplines to denote extent, scope, or a set of possible values. In mathematics, the range of a function is the set of all output values that the function can produce from its domain. Formally, for a function f: X → Y, the range is {f(x) : x ∈ X}. The range is also called the image of X under f and is distinct from the codomain, which is the target set Y.

In statistics and data analysis, the range refers to the spread of a data set and is defined as the difference between its maximum and minimum values. It provides a simple measure of how widely the values vary, though it is sensitive to outliers.

In geography, a mountain range is a connected series of mountains often forming a continuous crest or belt. The term can also appear in broader geographic descriptions to denote a linearity of high ground rather than a single peak.

In everyday usage, range appears in many contexts to indicate reach or capacity. For example, the range of a device or weapon describes the maximum distance over which it can operate or be effective, and a kitchen range refers to a cooking stove. The word also appears in commerce and services to denote the breadth of products or options offered.

In music, the range of an instrument or voice is the span between its lowest and highest pitches. Understanding range helps describe capabilities in performance and notation.