# Functions of literature review

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You can download the paper by clicking the button above. Enter the email address you signed up with and we’ll email you a reset link. In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. When the domain and the codomain are sets of numbers, each such pair may be considered as the Cartesian coordinates of a point in the plane. In general, these points form a curve, which is also called the graph of the function. This is a useful representation of the function, which is commonly used everywhere.

Functions are widely used in science, and in most fields of mathematics. Their role is so important that functions of literature review has been said that they are «the central objects of investigation» in most fields of mathematics. The red curve is the graph of a function, because any vertical line has exactly one crossing point with the curve. A function that associates any of the four colored shapes to its color. Formally speaking, it may be identified with the function, but this hides the usual interpretation of a function as a process. Therefore, in common usage, the function is generally distinguished from its graph.

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The range of a function is the set of the images of all elements in the domain. However, range is sometimes used as a synonym of codomain, generally in old textbooks. It is immediate that an arbitrary relation may contain pairs that violate the necessary conditions for a function, given above. Formally, functions may be identified to relations that are both univalent and left total. Violating the left-totality is similar to giving a convenient encompassing set instead of the true domain, as explained above. Various properties of functions and function composition may be reformulated in the language of relations.

The set of all functions from some given domain to a codomain is sometimes identified with the Cartesian product of copies of the codomain, indexed by the domain. This point of view is used for example in the discussion of a choice function. Note: infinite Cartesian products are often simply «defined» as sets of functions. There are various standard ways for denoting functions. The most commonly used notation is functional notation, which defines the function using an equation that gives the names of the function and the argument explicitly. This gives rise to a subtle point, often glossed over in elementary treatments of functions: functions are distinct from their values.

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Public Perceptions of the Police: Effects of Police Investigation and Police Resources By Andreas Cebulla, Recent case study Director at the National Centre for Social Research and Mike Stephens, Senior Lecturer in Criminology and Social Policy at Loughborough University, UK.

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