Knowledge organisers

Relations and Functions: CBSE Class 11 Maths knowledge organiser

Everything to know about relations and functions on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Cartesian product: A × B: all ordered pairs (a, b) with a in A and b in B.
Relation: Any subset of A × B.
Function: A relation in which every element of A has exactly one image in B.

Key formulas

Product	\(n(A\times B)=n(A)\,n(B);\) \(\text{relations }A\to B:\ 2^{n(A)n(B)}\)
Function: each element of the domain has exactly one image; domain: denominators ≠ 0, \(\sqrt{\ }\) of \(\ge0\)
\(\|x\|\ge0\); \(\operatorname{sgn}x\in\{-1,0,1\}\); \([x]\) = greatest integer \(\le x\) (\([-2.5]=-3\))

Worked example

Find the domain of \(f(x) = \dfrac{x}{x^2 - 9}\).

\(x^2 - 9 \neq 0\): domain \(\mathbb R - \{-3, 3\}\).

Common mistakes

Calling a relation a function when some element of the domain has two images, or none.
\([-2.5] = -2\): the greatest integer function goes down, to \(-3\).
Cancelling \(x - 2\) in \(\dfrac{x^2 - 4}{x - 2}\) and forgetting that \(2\) is still not in the domain.
Mixing up codomain and range.

You should be able to…

Work with ordered pairs and Cartesian products and recognise a function among relations.
Find domains and ranges of standard real functions and combine functions.
Analyse modulus, signum, greatest integer and rational functions fully, with their graphs in mind.
Reason about ranges of less obvious functions and about products of sets.

The printable sheet

Relations and Functions knowledge organiser for CBSE Class 11 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Relations and Functions knowledge organiser (CBSE Class 11 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 11 Maths topics: Sets · Trigonometric Functions · Complex Numbers and Quadratic Equations · Linear Inequalities · Permutations and Combinations · Binomial Theorem · Sequences and Series · Straight Lines · Conic Sections · Introduction to Three Dimensional Geometry · Limits and Derivatives · Statistics · Probability · All CBSE Class 11 Maths organisers