Relations and Functions

Functions

Have you ever thought that a particular person has particular jobs or functions to do? Consider the functions or roles of postmen. They deliver letters, postcards, telegrams and invites etc. What do firemen do? They are responsible for responding to fire accidents. In mathematics also, we can define functions. They are responsible for assigning every single object of one set to that of another.

Suggested Videos

Play
Play
Play
Play
Play
previous arrow
next arrow
previous arrownext arrow
Slider

 

Functions

A function is a relation that maps each element x of a set A with one and only one element y of another set B. In other words, it is a relation between a set of inputs and a set of outputs in which each input is related with a unique output. A function is a rule that relates an input to exactly one output.

functions

It is a special type of relation. A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B and no two distinct elements of B have the same mapped first element.  A and B are the non-empty sets. The whole set A is the domain and the whole set B is codomain.

Browse more Topics under Relations And Functions

Representation

A function f: X →Y is represented as f(x) = y, where, (x, y) ∈ f and x ∈ X and y ∈ Y.

For any function f, the notation f(x) is read as “f of x” and represents the value of y when x is replaced by the number or expression inside the parenthesis. The element y is the image of x under f and x is the pre-image of y under f.

functions

Every element of the set has an image which is unique and distinct. If we notice around, we can find many examples of functions.

If we lift our hand upward, it is a function. Waving our hand freely, it is a function.  A walk in a circular track, yes it is a type of function. Now you can think of other examples too! A graph can represent a function. The graph is the set of all pairs of the Cartesian product.

Does this mean that every curve in the world defines a function? No, not every curve drawn is a function. How to find it? Vertical line test. If any curve intercepts a vertical line at more than one point, it is a curve only not a function.

Solved Example for You

Question 1: Which of the following is a function?

1.Relation2.

3.Answer : Figure 3 is an example of function since every element of A is mapped to a unique element of B and no two distinct elements of B have the same pre-image in A.

Question 2: Give an example of a function?

Answer: An example of a function is the relationship x → x. The reason for this is that every element in x has a relation with y. Moreover, no element in x has two or more than two relationships.

Question 3: Explain what is a function and what is not?

Answer: A function refers to a relation such that every input has only one output. For example, y is a function of x and x is not a function of y (y = 9 consist of multiple outputs). Moreover, y is not a function of x (x = 1 consist of multiple outputs), x does not happen to be a function of y (y = 2 has multiple outputs).

Question 4: What is the classification of functions?

Answer: The classification of function takes place by the type of mathematical equation which shows their relationship. Some functions can be algebraic. Trigonometric functions like f(x) = sin x are those that involve angles. Some functions have logarithmic and exponential and logarithmic relationships and their classification are as such.

Question 5: What are basic polynomial functions?

Answer: (x) =c, f(x) =x, f(x) =x2, and f(x) =x3 are basic polynomial functions.

Share with friends

Customize your course in 30 seconds

Which class are you in?
5th
6th
7th
8th
9th
10th
11th
12th
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
tutor
tutor
Ashhar Firdausi
IIT Roorkee
Biology
tutor
tutor
Dr. Nazma Shaik
VTU
Chemistry
tutor
tutor
Gaurav Tiwari
APJAKTU
Physics
Get Started

2
Leave a Reply

avatar
1 Comment threads
1 Thread replies
2 Followers
 
Most reacted comment
Hottest comment thread
2 Comment authors
Eli SimeonAl quba Recent comment authors
  Subscribe  
newest oldest most voted
Notify of
Al quba
Guest
Al quba

The example for onto function doesn’t qualify as a function in the first place. Does it??
It is a relation but not a function because a single element in the domain has been mapped to two elements in the co domain. Isn’t it??
Please tell me if I’m correct or not.
It is really confusing.

Eli Simeon
Guest
Eli Simeon

An onto function exists if and only the co-domain is equal to the range that is every element in set A (the domain) is mapped to every element in set B (the range/codomain) i.e without leaving out any element. Irrespective of whether it is a one to one mapping or not. Therefore it is a function. Put simply, take set A as a set of sons and set B as a set of fathers, a function requires that every son has one father (which is normal) yet every father can have more than one son(which is also normal) so if… Read more »

Customize your course in 30 seconds

Which class are you in?
No thanks.