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Functions — Revision Notes

ICSE · Class 12 · Mathematics

Functions revision notes for ICSE Class 12 Mathematics: 4 topics in quick points. 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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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 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.
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.

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All ICSE Class 12 Mathematics Revision Notes

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