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What is a function?Description: What is a function?


Learn that a function is a mapping of a set of inputs connecting them to a set of ouputs. This can be described by a picture or by writing a set of couples.

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what is a function ?

A function is a mapping that takes inputs from a Domain and maps (sends) them to a outputs in a co-Domain.

So for example, the function "What country is this city the capital of ?"

With the Domain { Brussels, Dhaka, Brasilia }

And the co-Domain {The countries of the world }

The function: 

Takes the input 'Brussels' and maps it to the country 'Belgium'

It takes the input 'Dhaka' and maps it to the country 'Bangladesh'

It takes the input 'Brasilia' and maps it to the country 'Brasil'


The set of values {Belgium, Bangladesh, Brasil} that are 'hit' by the mapping from the co-Domain are called the Range.

The Range is a subset of the co-Domain.


So a function is a mapping from a set of inputs to a set of outputs.

In this question we are asked to map the inputs  { Brussels, Dhaka, Brasilia } to the outputs {Belgium, Bangladesh, Brasil}

and we list them in the form  { (input, output), (input2, output2), (input3, output3) }

So our answer is :  {  ( Brussels, Belgium),(Dhaka, Bangladesh), (Brasilia ,Brasil)  }


Example 2:  Given the Domain  { 1, 5, 7 } and the function "Double this number" and the co-Domain {The integers}

Write the function in the form: { (input, output), (input2, output2), (input3, output3) }

So :  1 -> 2, 5->10, and 7->14

So our answer is {(1,2), (5,10),(7,14)}