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Functions

ICSE · Class 12 · Mathematics

Quick revision notes for Functions — ICSE Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

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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Key Topics to Revise

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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.
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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.
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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.
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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.

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Full Notes

Key Concepts

A relation from a setThe domain is the set fromImportant examples include constantA function is oneA function is onto if every

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.

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