Language of functions

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

What are mappings?

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

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

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

Notation

• Functions are denoted by the notation?f(x),?g(x), etc
  • eg. f(x) = x²?- 3x + 2
• Of 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 ?, ?, ?, ?

• So ? is a?subset?of ? 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’

• 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

Range

• The?range?of a function is the set of values of all possible ‘outputs’
• The type of values in the range depend on the domain