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Concept Maps

Functions — Concept Maps

ICSE · Class 12 · Mathematics

4 concept maps of Functions for ICSE Class 12 Mathematics, each also written out as a text outline. Part of the ICSE Class 12 Mathematics syllabus.

101 questions30 flashcards14 formulas & key relations5 concepts

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A comprehensive infographic comparing different types of functions: one-one (injective), onto (surjective), many-one, into, and bijective, using set diagrams and clear definitions.
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4 Concept Maps

Functions Concept Hierarchy

Functions Concept Hierarchy

The map in words

  • Functions
    • Basic Concepts
      • Definition
      • Domain
      • Codomain
      • Range
    • Classification
      • Relation vs Function
      • Even vs Odd
      • Standard Functions
    • Properties
      • One-One Injective
      • Onto Surjective
      • Bijective
      • Invertible
    • Operations
      • Composition
      • Addition
      • Multiplication
      • Division
    • Advanced Topics
      • Inverse Functions
      • Compound Functions
      • Function Families
      • Graphical Analysis

Functions — Complete Chapter Overview

Functions — Complete Chapter Overview

The map in words

  • Functions
    • Definition
      • Every element of A
        • has exactly ONE image in B
      • f colon A to B
      • Relation that is a function
    • Key Terms
      • Domain
        • Set A
        • All inputs
      • Co-domain
        • Set B
        • All possible outputs
      • Range
        • Actual outputs
        • Subset of co-domain
    • Types of Functions
      • One-One Injective
        • Different inputs
        • Different outputs
        • n of A leq n of B
      • Onto Surjective
        • Range equals Co-domain
        • Every b has pre-image
        • n of A geq n of B
      • Bijective
        • Both one-one and onto
        • n of A equals n of B
        • Invertible
    • Standard Functions
      • Constant f of x equals k
      • Identity f of x equals x
      • Modulus f of x equals abs x
      • Floor Greatest Integer
      • Signum Sign function
      • Exponential b to x
      • Logarithmic log base b of x
    • Composition
      • g circ f means g after f
      • Apply f first then g
      • Not commutative
      • Is associative
    • Inverse
      • Only for bijections
      • f of x equals y iff x equals f inverse of y
      • f inverse circ f equals Identity
      • g circ f inverse equals f inverse circ g inverse

Functions - Concept Hierarchy and Classification

Functions - Concept Hierarchy and Classification

The map in words

  • Functions
    • Definition and Basics
      • Relations
      • Function criteria
      • Domain, Range, Codomain
    • Types of Functions
      • One-One Injection
        • Definition
        • Properties
        • Graphical test
      • Onto Surjection
        • Definition
        • Properties
        • Verification
      • Bijective
        • Both one-one and onto
        • Invertible
        • Correspondence
    • Real Functions
      • Polynomial
      • Rational
      • Square root
      • Modulus
      • Exponential
      • Logarithmic
    • Operations
      • Sum f+g
      • Difference f-g
      • Product fg
      • Quotient f/g
      • Composition f∘g
    • Inverse Functions
      • Definition
      • Conditions for invertibility
      • Finding inverses
      • Properties
      • Inverse of composition
    • Special Properties
      • Even functions
      • Odd functions
      • Domain restrictions

Functions as a special type of relation between two sets

Functions as a special type of relation between two sets

The map in words

  • Functions as a special type of relation between two sets
    • Function and relation
    • Domain, codomain, range
    • Real functions and standard real functions
    • Testing functions graphically
    • Types of functions
    • Counting functions between finite sets
    • Composition of functions
    • Inverse of an element

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Frequently Asked Questions

What are the important topics in Functions for ICSE Class 12 Mathematics?
Key topics in Functions include Basic idea of a function, Standard real functions and their graphs, Domain and range of real functions, Graphical tests. Study these first, then practise questions on each for the ICSE Class 12 board exam.
What do the concept maps for Functions show?
The 4 maps show how the ideas in Functions connect: Functions Concept Hierarchy; Functions — Complete Chapter Overview. Each map is also written out as an outline on this page.
How should I revise Functions for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 101 practice questions on Functions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Functions

All ICSE Class 12 Mathematics Concept Maps

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