Skip to main content
Super TutorResources
Chapter 2 of 13
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Syllabus

Functions

ICSE · Class 12 · Mathematics

Complete topic list for Functions in ICSE Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

101 questions30 flashcards5 concepts

Interactive on Super Tutor

Studying Functions? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for syllabus and more.

Try Super Tutor — Free

1,000+ Class 12 students started this chapter today

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

This is just one of 14+ visuals inside Super Tutor's Functions chapter

Explore the full set
4 Topics · ICSE Class 12 Mathematics

Topics in Functions

1

1. Basic idea of a function

  • A relation from a set A to a set B is a function only if every element of A has exactly one image in B.
  • A function can be written as f: A → B.
  • Domain is the set A, co-domain is the set B, and range is the set of all images of elements of A.
2

2. Standard real functions and their graphs

  • Constant function: f(x)=k for all x∈R; domain R, range {k}; graph is a line parallel to the x-axis.
  • Identity function: f(x)=x for all x∈R; domain R, range R; graph passes through the origin at 45° to the x-axis.
  • Polynomial function: f(x)=a0+a1x+...+anx^n for all x∈R, with real coefficients and non-negative integer n; domain R, range subset of R.
3

3. Domain and range of real functions

  • A real function must take real values for every input in its domain.
  • For rational functions, denominators must not be zero.
  • For square root expressions, the quantity under the square root must be non-negative.
4

4. Graphical tests

  • Graphical Test for Function: If any straight line parallel to the y-axis does not cut the curve at more than one point, then the curve represents a function.
  • Graphical Test for One-one Function: If any straight line parallel to the x-axis does not cut the graph of a function at more than one point, then the curve represents a one-one function.
  • The vertical line test checks whether a graph represents a function.

Key Concepts

Central concept: Functions as a special type of relation between two sets

Function and relationDomain, codomain, rangeReal functions and standard real functionsTesting functions graphicallyTypes of functionsCounting functions between finite setsComposition of functionsInverse of an element

Frequently Asked Questions

What are the important topics in Functions for ICSE Class 12 Mathematics?
Key topics in Functions include Functions Concept Hierarchy, Functions — Complete Chapter Overview, Functions - Concept Hierarchy and Classification. These are the concepts ICSE Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Functions — ICSE Class 12 Mathematics?
Understand the core concepts first, then work through the 101 practice questions available for this chapter. Revise formulas and 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 13 chapters — ICSE Class 12 Mathematics Syllabus

For serious students

Get the full Functions chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for ICSE Class 12 Mathematics.

Try Super Tutor Free
Try the full chapter — Free