IB DP Maths: AA HL复习笔记2.3.1 Language of Functions

What is a mapping?

• A mapping transforms one set of values (inputs) into another set of values (outputs)
• Mappings can be:
  • One-to-one
    • Each input gets mapped to exactly one unique output
    • No two inputs are mapped to the same output
    • For example: A mapping that cubes the input
  • Many-to-one
    • Each input gets mapped to exactly one output
    • Multiple inputs can be mapped to the same output
    • For example: A mapping that squares the input
  • One-to-many
    • An input can be mapped to more than one output
    • No two inputs are mapped to the same output
    • For example: A mapping that gives the numbers which when squared equal the input
  • Many-to-many
    • An input can be mapped to more than one output
    • Multiple inputs can be mapped to the same output
    • For example: A mapping that gives the factors of the input

What is a function?

• A function is a mapping between two sets of numbers where each input gets mapped to exactly one output
  • The output does not need to be unique

• One-to-one and many-to-one mappings are functions
• A mapping is a function if its graph passes the vertical line test
  • Any vertical line will intersect with the graph at most once

What notation is used for functions?

What are the domain and range of a function?

• The domain of a function is the set of values that are used as inputs

What are piecewise functions?

• Piecewise functions are defined by different functions depending on which interval the input is in
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