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Chapter Summary

Functions

ICSE · Class 12 · Mathematics

Summary of Functions for ICSE Class 12 Mathematics. Key concepts, important points, and chapter overview.

101 questions30 flashcards5 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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Overview

A function is a special type of relation in which every element of the domain has exactly one image in the co-domain. The chapter builds the idea of a function from basic mappings to real functions, then studies important types such as one-one, onto, and bijective functions. It also covers domain, c

Key Concepts

A relation from a set

A relation from a set A to a set B is a function if every element of A has exactly one image in B. A function is written as f: A → B.

The domain is the set from

The domain is the set from which inputs are taken, the co-domain is the target set, and the range is the set of all actual images. Range is always a s

Important examples include constant

Important examples include constant, identity, polynomial, rational, linear, square, square root, reciprocal, modulus, floor, ceiling, signum, exponen

A function is one

A function is one-one if different elements of the domain have different images. Equivalently, if f(a) = f(b), then a = b. The horizontal line test ch

A function is onto if every

A function is onto if every element of the co-domain has at least one pre-image in the domain. In this case, range equals co-domain.

Learning Objectives

  • Understand the meaning of a function as a special relation
  • Identify domain, co-domain, and range of a function
  • Classify functions as one-one, onto, or bijective
  • Use graphical tests to check whether a curve represents a function and whether it is one-one
  • Study standard real functions and their domains and ranges

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 Chapter Summary

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