The document discusses the concept of functions in mathematics, including dependent and independent variables, domain, codomain, range, and the vertical line test. It categorizes functions into four main types: one-to-one (injective), many-to-one, onto (surjective), and into functions, providing a brief definition for each. An example illustrates how to determine if a given function is one-to-one by checking the outputs for various inputs.

1. Function and its Types
by
Noor ul ain
MATHS TUTOR AT MYTUTORPOD(BS MATHEMATICS)

2. Do you find maths boring?

3. Table of content
 Function
 Dependent and independent variables
 Domain , codomain and range of a function
 Vertical line test to check the function
 When will function not exists?
 Types of functions
 One to one(injective) function
 Many to one function
 Onto(surjective) function
 Into function
 Example
 Quick overview

4. Function
f:AB is a rule by which each
element of A is associated with a
unique element of B.

5. Domain, Co-domain and Range of a
function

6. Conditions of function
1. Whole domain is used.
2. domain should not be used twice.

7. Dependent and independent variables
 y-dependent variable
 X- independent variable
in y=f(x)
Graph of a function

8. Verticle Line Test

9. When will function not exists?

10. Types of Function
There are four types of a function
1. One to one(injective) function
2. Many to one function
3. Onto(surjective) function
4. Into function

11. 1. One to One (Injective) function
every element of domain has a single image with codomain.

12. 2. Many to one function
One or more elements of domain have more than one image in
the codomain.

13. 3. Onto(Surjective) function
For every element of codomain there exists an element in domain.

14. 4. Into Function
Every element of codomain are not mapped with elements of domain.

15. Example:
check whether the function f(x)= 2x+3, is one to one or not if Domain
= {1,2,1/2} and Codomain ={5,7,4}
SOLuTION:
Putting 1,2,1/2 in place of x in f(x)=2x+3, we get:
f(1)=5
f(2)=7
f(1/2)=4
As, for every value of x we get a unique value of f(x) thus, we can conclude
that our function f(x) is one to one.

16. Quick overview: