# CLASS-11RELATION & FUNCTION - CONCEPT OF FUNCTION

FUNCTION -

Concept & Definition Of Function –

A) Function as a special type of relation

﻿Set A﻿                              Set B

1                                       1

-1

√3                                       3

- √3

2                                       4

- 2

3                                       9

- 3

In above picture, a number belonging to set A is associated to its square number in set B. As a result of this association, we obtained the set of ordered pairs P = {(1, 1), (-1, 1), (√3, 3), (-√3, 3), (2, 4), (-2, 4), (3, 9), (-3, 9)}

Set C                             Set D

1                                       1

-1

5                                      √3

- √3

7                                      √5

- √5

9                                       4

- 4

In above picture, a number belongings to set C is associated to its square root number in set D. as a result, we obtained the set of ordered pairs Q = {(1, 1), (1, -1), (5, √3), (5, -√3), (7, √5), (7, -√5), (9, 4), (9, -4)}

Observe the distinction between the diagrams of the two example. From pic-1 numbers from set-A more than one element is making pair with only one element of the same color from set-B, thus, yielding a set of ordered pair in which no two or more ordered pairs have the same first component.

From pic-2, only one element from set-C making pairs with more than one element of same color from set-D, thus, yielding a set of ordered pairs in which more than one ordered pair have the same first component such as (1, 1), (1, -1). Set of ordered pairs such as obtained in pic-1, in which no two ordered pairs have the same first component is called a function. The set of ordered pairs obtained in pic-2 is not a function. Thus, functions are special types of relations.