Language of Functions (CIE A Level Maths: Pure 1): Revision Note

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Language of Functions

Language of functions

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

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

Ā 

What are mappings?

  • A mapping takes an ā€˜inputā€™ from one set of values to an ā€˜outputā€™ in another

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

  • Mappings can be
    • ā€˜many-to-oneā€™ (many ā€˜inputā€™ values go to one ā€˜outputā€™ value)
    • ā€˜one-to-manyā€™
    • ā€˜many-to-manyā€™
    • ā€˜one-to-oneā€™

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 ā€˜inputā€™ value maps to a single ā€˜outputā€™
  • 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 ā†¦ x2 ā€“ 3x + 2

Sets of numbers

  • Functions often involve domains and ranges for specific sets of numbers
  • All numbers can be organised into different sets ā„•, ā„¤, ā„š, ā„

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

  • So ā„• is a subset of ā„¤ etc
  • ā„¤- 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 ā€˜inputā€™

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
  • RestrictionsĀ on a domain can turnĀ many-to-oneĀ functions intoĀ one-to-oneĀ functions

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

Ā 

Range

  • The range of a function is the set of values of all possible ā€˜outputsā€™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

Expertise: Maths

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 ā€“ if itā€™s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams ā€“ one of the many reasons he is excited to be a member of the SME team.