Relations and Functions — Part 2: One-one and onto functions: visual lesson, CBSE Class 12 Mathematics

Lesson

Relations and Functions, Part 2: Types of functions

Does every output come from exactly one input?

In this lesson you will

Recall what makes a relation a function
Decide whether a function is one-one (injective) or onto (surjective)
Prove that a real function is one-one, onto or bijective
See how the domain and codomain change the answer
Count one-one and onto functions between finite sets

$y = 2x + 3$
$y = 5$

Every horizontal line meets $y = 2x + 3$ exactly once.

Concept

What you will be able to do

Recall the definition of a function
Test one-one (injective) and onto (surjective)
Prove a real function is a bijection
See how the codomain changes "onto"
Count one-one and onto functions

Concept

A function: one arrow from each input

A function $f : A \to B$ assigns to each $x \in A$ exactly one $f(x) \in B$ . $A$ is the domain, $B$ the codomain, and $\{f(x) : x \in A\}$ the range.

A function: exactly one arrow leaves each element of $A$.

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