The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as the input) completely determines another quantity (the value, or output). A function associates a unique value to each input of a specified type. The argument and value may be real numbers, but they can also be elements from any given sets: the domain and codomain of the function. In addition to elementary functions on numbers, functions include maps between algebraic structures such as groups, and maps between geometric objects such as manifolds.

There are many ways to represent or visualize functions: a function may be described by a formula, by a plot or graph, by an algorithm that computes it, or by a description of its properties. Sometimes, a function is described through its relationship to other functions (for example, inverse functions). In applied disciplines, functions are frequently specified by tables of values or by formulas. In pure mathematics, functions are defined using set theory, and there are theorems that show the existence of uncountably many different functions, most of which cannot be expressed with a formula or algorithm.

In a setting where outputs of functions are numbers, functions may be added and multiplied, yielding new functions. Collections of functions with certain properties, such as continuous functions and differentiable functions, usually closed under certain operations, are called function spaces and are studied as objects in their own right in real analysis. An important operation on functions, that distinguishes them from numbers, is composition of functions. The composite function is obtained by using the output of one function as the input of another. This operation provides the theory of functions with its most powerful structure.

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Non relativistic mass velocity and time also give the following Hence change in rocket velocity is a function of effective exhaust velocity and time change of rocket mass and fuel mass

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