Functions

Functions

1.1

Functions

\(\blacksquare\) 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 \(Y\).

Example:


\(\blacksquare\) A function can be written as \(f:x \rightarrow 3x\) or \(f(x)=3x\), where \(x\) is the object and \(3x\) is the image.

\(\blacksquare\) Only one-to-one relation and many-to-one relation are functions.

\(\blacksquare\) When a graph is given, vertical line test can be used to determine whether the graph is a function.

Example:

Function


Not a function


Given an arrow diagram of a function:


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 \(9\).