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?

What is an inverse function?

• Only one-to-one?functions have inverses
• A function has an inverse if its graph passes the?horizontal line test
  • Any?horizontal line?will intersect with the graph?at most once

What are the connections between a function and its inverse function?

• The?domain of a function?becomes the?range of its inverse
• The?range of a function?becomes the?domain of its inverse

What are piecewise functions?

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