CIE A Level Maths: Pure 1

Revision Notes

1.3.1 Language of Functions

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Language of Functions

Language of functions

  • The language of functions has many keywords associated with it that need to be understood 

Language of Functions Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

What are mappings?

  • A mapping takes an ‘input’ from one set of values to an ‘output’ in another

 Language of Functions Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes 

  • Mappings can be
    • many-to-one’ (many ‘input’ values go to one ‘output’ value)
    • one-to-many’
    • many-to-many’
    • one-to-one’

Language of Functions Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes

What is the difference between a mapping and a function?

  • A function is a mapping where every ‘input’ value maps to a single ‘output’
  • Many-to-one and one-to-one mappings are functions
  • Mappings which have many possible outputs are not functions

Language of Functions Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes

Notation

  • Functions are denoted by the notation f(x), g(x), etc
    • eg. f(x) = x2 - 3x + 2
  • Or the alternative notation
    • eg. f : x ↦ x2 – 3x + 2

Sets of numbers

  • Functions often involve domains and ranges for specific sets of numbers
  • All numbers can be organised into different sets ℕ, ℤ, ℚ, ℝ

 Language of Functions Notes Diagram 5, A Level & AS Level Pure Maths Revision Notes 

  • So ℕ is a subset of ℤ etc
  • - would be the set of negative integers only

Domain

  • The domain of a function is the set of values that are allowed to be the ‘input’

Language of Functions Notes Diagram 6, A Level & AS Level Pure Maths Revision Notes

  • A function is only fully defined once its domain has been stated
  • Restrictions on a domain can turn many-to-one functions into one-to-one functions

EXTRA No1, A Level & AS Level Pure Maths Revision Notes

 

Range

  • The range of a function is the set of values of all possible ‘outputs’Language of Functions Notes Diagram 7, A Level & AS Level Pure Maths Revision Notes
  • The type of values in the range depend on the domain

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Worked example

Language of Functions Example Diagram, A Level & AS Level Pure Maths Revision Notes

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Paul

Author: Paul

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.