Editing Identity function (section)

{{short description|In mathematics, a function that always returns the same value that was used as its argument}}
{{distinguish|Null function|Empty function}}
[[image:Function-x.svg|thumb|[[Graph of a function|Graph]] of the identity function on the [[real number]]s]]

In [[mathematics]], an '''identity function''', also called an '''identity relation''', '''identity map''' or '''identity transformation''', is a [[function (mathematics)|function]] that always returns the value that was used as its [[argument of a function|argument]], unchanged. That is, when {{mvar|f}} is the identity function, the [[equality (mathematics)|equality]] {{math|1=''f''(''x'') = ''x''}} is true for all values of {{mvar|x}} to which {{mvar|f}} can be applied.