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((Sidebar
 | name = Functions

 | titlestyle = letter-spacing:0.0125em; background-color:#FFCC99
 | title = [[Function (mathematics)|Function]]

 | image = ((math|''x'' ↦ ''f''&thinsp;(''x'')|size=250%))

 | headingstyle = font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px

 | heading1 = [[History of the function concept]]

 | heading2 = Examples of [[domain of a function|domains]] and [[codomain]]s
 | content1style = text-align: left; padding-left: 1.5em;
 | content2 = ((plainlist|1=
* ((nowrap|1=<span title="arbitrary set" style="color:gray; padding-right: 0.3em"><math>X</math></span> <!-- space before comment deliberate
--><span style="font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em">[[Boolean-valued function|→]]</span> <!--
--><span title="Codomain of Booleans" style="padding: 0 0.3em"><math>\mathbb{B}</math>,</span> <!--
--><span title="Domain of Booleans" style="padding: 0 0.3em"><math>\mathbb{B}</math></span> <!--
--><span style="font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em">[[Ordered pair|→]]</span> <!--
--><span title="arbitrary set" style="color:gray; padding: 0 0.3em;"><math>X</math>,</span> <!--
--><span title="several Boolean variables" style="padding: 0 0.3em"><math>\mathbb{B}^n</math></span> <!--
--><span style="font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em">[[Boolean function|→]]</span> <!--
--><span title="Codomain of natural numbers" style="padding-left: 0.3em"><math>X</math></span>))
* ((nowrap|1=<span title="arbitrary set" style="color:gray; padding-right: 0.3em"><math>X</math></span> <!--
--><span style="font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em">[[integer-valued function|→]]</span> <!--
--><span title="integers" style="padding: 0 0.3em"><math>\Z</math>,</span> <!--
--><span title="integers" style="padding: 0 0.3em"><math>\Z</math></span> <!--
--><span style="font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em">[[sequence|→]]</span> <!--
--><span title="arbitrary set" style="color:gray; padding-left: 0.3em"><math>X</math></span>))
* ((nowrap|1=<span title="arbitrary set" style="color:gray; padding-right: 0.3em"><math>X</math></span> <!--
--><span style="font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em">[[real-valued function|→]]</span> <!--
--><span title="real numbers" style="padding: 0 0.3em"><math>\Reals</math>,</span> <!--
--><span title="real numbers" style="padding: 0 0.3em"><math>\Reals</math></span> <!--
--><span style="font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em">[[function of a real variable|→]]</span> <!--
--><span title="arbitrary set" style="color:gray; padding: 0 0.3em"><math>X</math>,</span> <!--
--><span title="real coordinate (or Euclidean) space" style="padding: 0 0.3em"><math>\R^n</math></span> <!--
--><span style="font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em">[[function of several real variables|→]]</span> <!--
--><span title="arbitrary set" style="color:gray; padding-left: 0.3em"><math>X</math></span>))
* ((nowrap|1=<span title="arbitrary set" style="color:gray; padding-right:0.3em"><math>X</math></span> <!--
--><span style="font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em">[[complex-valued function|→]]</span> <!--
--><span title="complex numbers" style="padding: 0 0.3em"><math>\Complex</math>,</span> <!--
--><span title="complex numbers" style="padding: 0 0.3em"><math>\Complex</math></span> <!--
--><span style="font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em">[[function of a complex variable|→]]</span> <!--
--><span title="arbitrary set" style="color:gray; padding: 0 0.3em"><math>X</math>,</span> <!--
--><span title="complex coordinate space" style="padding: 0 0.3em"><math>\Complex^n</math></span> <!--
--><span style="font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em">[[Function of several complex variables|→]]</span> <!--
--><span title="arbitrary set" style="color:gray; padding-left: 0.3em"><math>X</math></span>))
))

 | heading3 = [[function space|Classes/properties]] 
 | content3 = ((flatlist|
* [[Constant function|Constant]]
* [[Identity function|Identity]]
* [[Linear map|Linear]]
* [[Polynomial]]
* [[Rational function|Rational]]
* [[Algebraic function|Algebraic]]
* [[Analytic function|Analytic]]
* [[Smooth function|Smooth]]
* [[Continuous function|Continuous]]
* [[Measurable function|Measurable]]
* [[Injective function|Injective]]
* [[Surjective function|Surjective]]
* [[Bijection|Bijective]]
))

 | heading4 =  Constructions
 | content4 = ((flatlist|
* [[Restriction (mathematics)|Restriction]]
* [[function composition|Composition]]
* [[Lambda calculus|λ]]
* [[Inverse function|Inverse]]
))

 | heading5 =  Generalizations  
 | content5 = ((flatlist|
* [[Binary relation]]
* [[Partial function|Partial]]
* [[Multivalued function|Multivalued]]
* [[Implicit function|Implicit]]
* [[Function space|Space]]
))
))<noinclude>

==See also==
((Math templates|boxes))

[[Category:Mathematics sidebar templates]]
</noinclude>

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