A function assigns exactly one output to each input. This course builds functions from Cartesian products and relations and studies the standard real functions.
The course follows the NCERT Class 11 Mathematics chapter Relations and Functions and has 3 lessons. Each lesson explains the ideas with worked examples and ends with practice questions and full answers. The numbers in every example and question are our own, so the lessons can be used alongside the textbook exercises.
- Cartesian Products and Relations — Ordered pairs, Cartesian products, relations with domain, codomain and range, and counting relations.
- Functions and Their Graphs — Functions as special relations, the standard real functions with domains and ranges, and the algebra of functions.
- Relations and Functions: Mixed Practice — Twelve original questions on products, relations and real functions, with answers.
By the end you will be able to:
- Form Cartesian products and count relations.
- Find the domain, codomain and range of a relation.
- Decide whether a relation is a function.
- Find domains and ranges of real functions and combine functions.