What are Functions ? - Class 12 maths chapter 1 - Relations and Functions

 

WHAT ARE FUNCTIONS?

 

So in the previous post, we learnt about “ RELATIONS”. If you missed those posts kindly follow the link, as it is pre requisite knowledge to study functions.

CLICK THIS LINK

WHAT ARE RELATIONS? 

 

Dear friends

“ FUNCTIONS” are special type of “RELATIONS”

In a Relation we associate elements of set “A” (DOMAIN) with the elements of set  “B”   ( CO DOMAIN) following a fixed rule.

R = { (0,0), ( 1, -1) , (1, 1) , ( 4, -2) , ( 4, 2) , ( 9, -3) , ( 9, 3) }

See how 1 associated with -1 and 1 in red colour.

4 with -2 and 2 in blue and 9 with -3 and 3 in green.

R = { (0,0), (-1,1), (1,1), (-2,4) , ( 2,4), ( -3,9) , ( 3,9), ( -4,16), (4,16) }

See how -1 and 1 are associated with 1 in yellow colour

-2 and 2 with 4 in green ; -3 and 3 with 9 in red and -4 and 4 with 16 in black

Now, we’ll take just one more example and then we can understand what functions are

See how each -2 is connected with -1 only, -1 with 0 only, 0 with 1 only and so on.

 

 

 

Now see, in the e.g.1  first diagram we have associations like this

In e.g.2 second diagram , association is like this

In e.g.3 third diagram , association is like this

“Relations” in which elements have association of type 2 and type 3 are termed as “Functions”

In other words

The RELATIONS in which each element of the DOMAIN are related with one and only one element in the CODOMAIN are termed as FUNCTIONS.

 

See in e.g. 1

“ 4” ( element of DOMAIN) is related to two elements -2 and 2 ( elements of CODOMAIN). Similarly , 1 is associated with -1 and 1

Therefore this relation is not a function.

Let us understand it more with one question:

Question

Which of the following relation is a function? 

A = { (1,a), (2,b), (3,c), (1,d)}                    B = { (1,a), (1,b), (2,c), (2,d), (3,c), (3,d)}

C = { (1,a) , (2,a), (3,a),(4,b)}                    D = { (1,a), (2, a), (3,a), (1,b)}

 Take some time and try to solve it using diagram

A 

Not a function because 1 is associated with two elements “a” and “d”

B     

Not a function because 1 is associated with two elements “a” and “b”

                                     2 is associated with two elements “c” and “d”

                                     3 is associated with two elements “c” and “d”

C   

It is a function1 is associated with only a

                           2 is associated with only a

                           3 is associated with only a

                          4 is associated with inly b

 

NOTE : elements of CODOMAIN can associate with any number of elements of domain but restriction is only on DOMAIN elements. Each domain element should associate with one and only one element of the CODOMAIN.

D 

Not a function because 1 is associated with two elements “a” and “b”

 

So, in this post I guess this much knowledge is enough.

In the next post we’ll see Functions with a different prospective and you’ll come to know more about functions.

click on the link below to see functions with a different linse.

What are functions ?- Part 2

Till then take care, Keep studying Maths and stay blessed.😄😄🙋🙋