What are Functions ? - Part 2 / Class 12 maths

 What are Functions – II ?

Hello everyone,

So, in the previous post I explained the meaning of Functions. If you missed the post, just click on the following link

 

 

Now, we’ll see Functions in more details:

A function is a process (or a relation) that associates each element x of a set X, the DOMAIN of the function, to a single element y of another set Y (possibly the same set), the CODOMAIN of the function.

Now you know why it is called “FUNCTION” ?

Because it does something, it’s a process.

 

I some times see FUNCTIONS as some kind of machine in which when we put some value of x of set X ( DOMAIN) and in return it gives a single value y of set Y ( CODOMAIN)

This was just a general presentation friends now let us see some real functions too.

So as in Real life we have different gadgets to fulfill our daily needs, similarly to fulfill our mathematical needs there are many types of functions. Let us discuss one such function

So, after this much study of modulus function, we can also represent it like this

F = {(0,0), (-1,1), (1,1), (-2,2) , (2,2) , (-3,3), (3,3),……. }

Note: Range elements are those elements of codomain which are associated with the elements of Domain, In General Domain elements are denoted by x and elements of Range are denoted by y

 

Can we draw a graph for it?

If we take terms before “ ,” as values of x ( Domain element)

If we take terms after “ ,” as values of y ( Range element)

See at the left side of the image. All the points of the function

f = {(0,0), (-1,1), (1,1), (-2,2) , (2,2) , (-3,3), (3,3),…….}

         O        D         A         E           B          F         C

 are marked on the graph paper and after joining those points we got “ V “ shaped graph.

 

Similarly there are more functions:

 Greatest integer function [x] , signum function etc.

So, dear students we have studied function in a new prospective and soon we'll be studying types of functions and composition.

For this post I guess this much is enough 😊😊

Bie