- Accounting Homework Help
- Biology Homework Help
- Chemistry Homework Help
- Computer Science Help
- Economics Homework Help
- Engineering Homework Help
- English Homework Help
- Essay Writing Services
- Finance Homework Help
- Management Homework Help
- Math Homework Help
- Matlab Programming Help
- Online Exam Help
- Online Quiz Help
- Physics Homework Help
- Statistics Homework Help

- Physics Assignment Help
- Chemistry Assignment Help
- Math Assignment Help
- Biology Assignment Help
- English Assignment Help
- Economics Assignment Help
- Finance Assignment Help
- Statistics Assignment Help
- Accounting Assignment Help
- Computers Assignment Help
- Engineering Assignment Help
- Management Assignment Help

Define the term function with the help of an appropriate example

A function is something that associates each element of a set with an element of another set (which may or may not be the same as the first set). The concept of function appears quite often even in non-technical contexts. For example, a social security number uniquely identifies the person, the income tax rate varies depending on the income, and the final letter grade for a course is often determined by test and exam scores, homeworks and projects, and so on.

In all these cases to each member of a set (social security number, income, tuple of test and exam scores, homeworks and projects) some member of another set (person, tax rate, letter grade, respectively) is assigned.

As you might have noticed, a function is quite like a relation. In fact, formally, we define a function as a special type of binary relation.

Definition (function): A function, denote it by f, from a set A to a set B is a relation from A to B that satisfies

1. for each element a in A, there is an element b in B such that <a, b> is in the relation, and

2. if <a, b> and <a, c> are in the relation, then b = c .

The set A in the above definition is called the domain of the function and B its codomain.

Thus, f is a function if it covers the domain (maps every element of the domain) and it is single valued.

The relation given by f between a and b represented by the ordered pair <a, b> is denoted as f(a) = b , and b is called the image of a under f .

The set of images of the elements of a set S under a function f is called the image of the set S under f, and is denoted by f(S) , that is,

f(S) = { f(a) | a ∈ S }, where S is a subset of the domain A of f .

The image of the domain under f is called the range of f.

Example: Let f be the function from the set of natural numbers N to N that maps each natural number x to x2. Then the domain and co-domain of this f are N, the image of, say 3, under this function is 9, and its range is the set of squares, i.e. { 0, 1, 4, 9, 16, ....} .