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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
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?
Exam Tip
Worked Example
Inverse Functions
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
Exam Tip
Worked Example
Piecewise Functions
What are piecewise functions?
Piecewise functions
are defined by different functions depending on which interval the input is in
Worked Example
b)state the domain.
转载自savemyexams
Previous post: IB DP Maths: AI SL复习笔记2.1.1 Equations of a Straight Line
Next post: IB DP Maths: AI SL复习笔记2.2.2 Graphing Functions
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