RELATION AND FUNCTION

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RELATION AND FUNCTION by Mind Map: RELATION AND FUNCTION

1. Introduction

1.1. A set is a collection of well-defined objects.

1.2. Relations and Functions.

1.3. “cartesian product”

2. Ordered Pair

2.1. Observe the seating plan in an auditorium To help orderly occupation of seats, tokens with numbers such as (1,5), (7,16), (3,4), (10,12) etc.

2.2. Example 1,1,1.2,1.3

3. Cartesian Product

3.1. Vegetables (A) Fruits (B) Carrot (c) Apple (a) Brinjal (b) Orange (o) Ladies finger (l) Grapes (g) Strawberry (s)

3.2. Definition If A and B are two non-empty sets, then the set of all ordered pairs (a, b) such that a AÎ , b B Î is called the Cartesian Product of A and B, and is denoted by A B ́ . Thus, A B ́ = ∈ {(a b, )| , a A b B ∈ } (read as A cross B). Also note that A × f =f

4. Relations

4.1. Definition Let A and B be any two non-empty sets. A ‘relation’ R from A to B is a subset of A B ́ satisfying some specified conditions. If x AÎ is related to y B Î through R , then we write it as x Ry. x Ry if and only if ( , x y) Î R .

5. Functions

5.1. Definition A relation f between two non-empty sets X and Y is called a function from X to Y if, for each x X Î there exists only one y YÎ such that ( , x y) Î f . That is, f ={(x,y)| for all x ∈ X, y ∈Y }.

6. Representation of Functions

7. Types of Functions

7.1. (i) one – one (ii) many – one (iii) onto (iv) into

8. Special Cases of Functions

9. Composition of Functions

9.1. Definition Let f A: ® B and g B: ® C be two functions (Fig.1.42). Then the composition of f and g denoted by g f  is defined as the function g f  ( ) x g = ( (f x)) ∀ x AÎ .

10. Identifying the Graphs of Linear, Quadratic, Cubic and Reciprocal Functions