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FUNCTIONS 

 

Class 10 Notes 

 Introduction: Function is an interesting

branch of mathematics. It helps in the study

of performance of a quantity lender various

conditions. Let’s see the difference between

function and relation.  

 Difference between function and relation: 

Function Relation

A function is a “well

behaved” relation. It

means it satisfies/has

a condition to move

from Domain to

Range.

A relation is just

a relationship

between sets of

information.

Function must use all

the elements in its

domain.

Relation can

have few

elements left out

in Domain.

 Now that we saw the difference between a

function and a relation. Let us now gain a

knowledge of necessary information

regarding fuction.  

 Types of intervals: Let a, b R and a<b.

Then

1. is called open

interval.  

 

 

2. is called

closed interval.  

 

 

3. is called left

open right closed interval. 

 

 

4. is called left

closed right open interval. 

  

5.  

  

6.  

  

7.  

  

8.  

 

9.  

 

 

 

 

4.  (i) If   , then  (ii) If   then 

 

5. (i) If  are even then   is even 

    (ii) If  are odd then   is even 

    (iii) If  is even function and  is an odd function then   is an odd function. 

6. (i)   

    (ii)   

    (iii)    

    (iv)   

 

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