## At A Glance

### Types Of Functions

Check us out at http://www.tutorvista.com//videos 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 the output). A function assigns a unique value to each input of a specified type. The argument and the value may be real numbers, but they can also be elements from any given sets: the domain and the codomain of the function. An example of a function with the real numbers as both its domain and codomain is the function f(x) = 2x, which assigns to every real number the real number that is twice as big. In this case, we can write f(5) = 10. In addition to elementary functions on numbers, functions include maps between algebraic structures like groups and maps between geometric objects like manifolds. In the abstract set-theoretic approach, a function is a relation between the domain and the codomain that associates each element in the domain with exactly one element in the codomain. An example of a function with domain {A,B,C} and codomain {1,2,3} associates A with 1, B with 2, and C with 3. There are many ways to describe or represent functions: by a formula, by an algorithm that computes it, by a plot or a graph. A table of values is a common way to specify a function in statistics, physics, chemistry, and other sciences. A function may also be described through its relationship to other functions, for example, as the inverse function or a solution of a differential equation. There are uncountably many different functions from the set of natural numbers to itself, most of which cannot be expressed with a formula or an 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 required to be closed under certain operations, are called function spaces and are studied as objects in their own right, in such disciplines as real analysis and complex analysis. An important operation on functions, which 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. Types of Function: Composite Functions Even and Odd Functions Inverse Functions Linear, Quadratic, and Cubic Functions Monotonic Functions Periodic Functions
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