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IB DP Maths: AI SL复习笔记2.2.1 Functions

Category: IB课程, 教材笔记, 福利干货 Date: 2022年7月19日上午10:55

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

2.8.1-Language-of-Functions-Notes-Diagram-2

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

2.8.1-Language-of-Functions-Notes-Diagram-4

2.8.1-Language-of-Functions-Notes-Diagram-5

2-2-1-ib-ai-sl-language-of-functions-a-we-solution

2-2-1-ib-ai-sl-language-of-functions-b-we-solution

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