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AQA A Level Maths: Pure复习笔记2.8.1 Language of Functions
Category:
A-level课程
,
教材笔记
,
福利干货
Date: 2022年7月27日 下午4:09
Language of Functions
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 ℕ, ℤ, ℚ, ℝ
So ℕ is a subset of ℤ etc
ℤ- 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
Worked Example
转载自savemyexams
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