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Functions

1.1 Functions
 
Definition
  • A function from set \(X\) to set \(Y\) is a special relation that maps each element \(x\) in set \(X\) to only one element \(y\) in set \(Y\).
 
The image illustrates the concept of a function using a central circle labeled ‘FUNCTION.’ Surrounding the central circle are three clouds with different labels and arrows pointing towards the central circle. The first cloud, labeled ‘RELATION,’ lists ‘ONE-TO-ONE’ and ‘MANY-TO-ONE.’ The second cloud, labeled ‘EQUATION,’ shows the equations ‘f: x → 3x’ and ‘f(x) = 3x.’ The third cloud, labeled ‘GRAPH,’ mentions ‘TESTED USING VERTICAL LINE TEST.’ The Pandai logo is present at the bottom right corner.
 
Example Function (One-to-one)
The diagram shows an illustration of two sets, namely set x and set y, connected by a one-to-one relationship
 
Graph
Function

Graph displaying a point and line, illustrating a one-to-one function with the vertical line test applied.
Not a function

A non-function graph with a circle intersecting a vertical line, function for example does not pass the vertical line test.
 
Example

Given an arrow diagram of a function:

Image of two unique numbers on square, showcasing one-to-one mapping in function f(x) = x^2.

  • Domain \(=\lbrace1,\,2, \, 3,\,5 \rbrace\)
  • Codomain \(=\lbrace1,\,4, \, 9,\,16,\,25 \rbrace\)
  • Range \(=\lbrace1,\,4, \, 9,\,25 \rbrace\)
  • Object of \(4\) is \(2\).
  • Image of \(3\) is \(9\).
 
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.

Functions

1.1 Functions
 
Definition
  • A function from set \(X\) to set \(Y\) is a special relation that maps each element \(x\) in set \(X\) to only one element \(y\) in set \(Y\).
 
The image illustrates the concept of a function using a central circle labeled ‘FUNCTION.’ Surrounding the central circle are three clouds with different labels and arrows pointing towards the central circle. The first cloud, labeled ‘RELATION,’ lists ‘ONE-TO-ONE’ and ‘MANY-TO-ONE.’ The second cloud, labeled ‘EQUATION,’ shows the equations ‘f: x → 3x’ and ‘f(x) = 3x.’ The third cloud, labeled ‘GRAPH,’ mentions ‘TESTED USING VERTICAL LINE TEST.’ The Pandai logo is present at the bottom right corner.
 
Example Function (One-to-one)
The diagram shows an illustration of two sets, namely set x and set y, connected by a one-to-one relationship
 
Graph
Function

Graph displaying a point and line, illustrating a one-to-one function with the vertical line test applied.
Not a function

A non-function graph with a circle intersecting a vertical line, function for example does not pass the vertical line test.
 
Example

Given an arrow diagram of a function:

Image of two unique numbers on square, showcasing one-to-one mapping in function f(x) = x^2.

  • Domain \(=\lbrace1,\,2, \, 3,\,5 \rbrace\)
  • Codomain \(=\lbrace1,\,4, \, 9,\,16,\,25 \rbrace\)
  • Range \(=\lbrace1,\,4, \, 9,\,25 \rbrace\)
  • Object of \(4\) is \(2\).
  • Image of \(3\) is \(9\).
 
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.
Chapter : Functions
Topic : Functions
Form 4 Additional Mathematics
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