Math major from IISER Trivandrum. Cleared JEE mains and advanced in 2015. I hope to make you fall in love with the subject just the way I do

Deeksha Chandana

Deeksha will be discussing about what a relation is, see a few types of relations, define a function and then try to graph some functions. You will later see composition of functions, binary mappings, inverse functions etc.

IIT JEE 2020 and 2021 Main and Advanced exam preparation. Know about detailed syllabus, best books, exam pattern and dates. Cover previous year question papers and book solutions from great educators.

IIT JEE

JEE Main and Advanced Preparation

English

Relations and Functions

Learn about types of functions like into - onto function, one to one function, bijective function, injective function, surjective function, periodic function, drawing graphs of mathematical functions.

Functions & Graphs

Functions and Their Graphs

Mathematics

IITJEE, NEET UG and Foundation

Ace the toughest competitive and government exams in India 

Test Preparation

A brief introduction video to the course. I have mentioned what are the topics that would be covered in this course.

Introduction to the Course

Some basic definitions. I started of with the definition of Cartesian product of sets and then defined what a relation is. We even discussed a few examples and then saw what an empty relation and a universal relation is.

Cartesian Product of Sets and the Defining Relations

Defining types of relations, i.e., reflexive, symmetric and transitive relations. Definition of equivalence relation and an example of equivalence relation which is congruence modulo relation.

Types of Relations: Equivalence Relation

Defining equivalence classes using the example of congruence modulo relation. Introducing to the concept of partitions of a Set.

Equivalence Classes (Congruence Modulo Example)

Discussion of properties of the congruence modulo m, and then see an application of the above relation.

Application of Congruence Modulo Relation

Another example of the way congruence modulo notation simplifies very tough and complicated looking problems.

Another Example Using the Congruence Modulo Definition

Basic introduction to the concepts of functions. Can be easily understood by any first timer and you would need good understanding of these definitions for understanding later videos. I have also included graphs of some functions which you would be encountering. I recommend you to remember the definition of those special functions, i.e., modulus function, step/greatest integer function, fractional part of x and signum function.

Introduction to Functions - Part 1

Continuation to the previous video on introduction to functions. I couldn't complete the algebra of real functions in the previous video, so I made this video for that purpose. And I also rushed through the last few graphs without explaining them in much detail in the previous video, so I repeated them in this video.

Introduction to Functions - Part 2

Introduction to types of functions, i.e., injective, surjective and bijective functions.

Injective, Surjective and Bijective Functions

I have given few examples of using horizontal line tests for graphs of functions to determine whether it is injective or surjective or not. I have later defined the composition of two functions.

Horizontal Line Tests and Composition of Functions

Discussion of a few theorems and one example in composition of functions. Discussion about inverse of a function and an theorem regarding that.

Composition and Inversions of Functions

Transformation of graphs. How do graphs change when we multiply the function with a scalar or add a scalar to the function. We will discuss this change of the graph of the function with respect to the original graph rather than separately calculating points and plotting them.

Transformation of Graphs

Discussing how to compute the composition of functions when you are encountered with split functions. That is how you do the composition by keeping track of the domains.

Composition of Split Functions

Discussion about even and odd functions, their examples. Decomposition of any function into an even and an odd function. Even and odd extensions of functions defined only for positive values.

Even and Odd Functions

Introduction to and importance of functional equations. Periodic functions and an example, fundamental periods of some, commonly encountered functions.

Functional Equations and Periodic Functions

A problem on using the concepts of periodic functions.

Problem Based on Periodic Functions

A Game Changer in Mathematics, produced multiple 100 percentilers, Air 33 & 34 (Main 2024), his courses are the Benchmark for IIT JEE 

Vineet Loomba

In this course, the educator targets the relations and binary operation part of Class Board exam. This is an important topic for boards. The course has been explained in the simplest manner as students find this topic a bit difficult.

Relations and Binary Operations: IIT JEE

Ashish Bajpai

Mastering Function For IIT JEE is a course where we will formally define Functions and terms related to Functions. We will categorize functions such as Onto / Into Function, One - One / Many - One Function , Odd and Even Function . We will understand about Periodic Functions and will learn how to find Period of Function.We will understand what are composite Functions and we will solve loads of problems on each topic so that students feel comfortable in chapter Functions. This is fourth part of overall courses on Functions. This course should be done after going through other parts such as courses on graphs and domain and range of function.

(Hindi) Mastering Functions For IIT JEE

Education:-B.Tech from NIT SURAT,
teaching experience:-6+ years offline,
mentoring more than 2000 students for IIT-JEE.

Meva Ram 

This Comprehensive detailed course of Function is prepared according to IIT-JEE syllabus and covered all the subtopics from basic with many more Illustrations and PYQ.

(Hindi) Comprehensive Function for IIT-JEE ( Mains and Advanced)

B.tech Mechanical DTU ,
Cleared major Engineering Entrances 
like IIT-JEE , BITSAT , CBSE 94.8%
Cleared NDA , SSC CHSL 
Educator and Learner

Abhishek Bhardwaj

This course is about Graphs which are used to solve problems in maths effectively and easily. This course is aimed to provide beginner to medium level understanding of graphs.

Lessons

16 lessons • 3h 11m

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Introduction to the Course

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Cartesian Product of Sets and the Defining Relations

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Types of Relations: Equivalence Relation

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Equivalence Classes (Congruence Modulo Example)

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Application of Congruence Modulo Relation

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Another Example Using the Congruence Modulo Definition

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Introduction to Functions - Part 1

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Introduction to Functions - Part 2

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Injective, Surjective and Bijective Functions

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Horizontal Line Tests and Composition of Functions

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