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data-event-name="pinnable-header.vector-toc.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">dölj</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inledning</div> </a> </li> <li id="toc-Etymologi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Etymologi"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Etymologi</span> </div> </a> <ul id="toc-Etymologi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Intuitiv_introduktion" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Intuitiv_introduktion"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Intuitiv introduktion</span> </div> </a> <ul id="toc-Intuitiv_introduktion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Definition" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definition"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Definition</span> </div> </a> <ul id="toc-Definition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Formell_definition" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formell_definition"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Formell definition</span> </div> </a> <ul id="toc-Formell_definition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Exempel_på_funktioner" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Exempel_på_funktioner"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Exempel på funktioner</span> </div> </a> <ul id="toc-Exempel_på_funktioner-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Typer_av_funktioner" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Typer_av_funktioner"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Typer av funktioner</span> </div> </a> <ul id="toc-Typer_av_funktioner-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Se_även" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Se_även"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Se även</span> </div> </a> <ul id="toc-Se_även-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Källor" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Källor"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Källor</span> </div> </a> <ul id="toc-Källor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externa_länkar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externa_länkar"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Externa länkar</span> </div> </a> <ul id="toc-Externa_länkar-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Innehåll" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Växla innehållsförteckningen" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Växla innehållsförteckningen</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Funktion</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Gå till en artikel på ett annat språk. Tillgänglig på 120 språk" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-120" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">120 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Funksie" title="Funksie – afrikaans" lang="af" hreflang="af" data-title="Funksie" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Funktion_(Mathematik)" title="Funktion (Mathematik) – schweizertyska" lang="gsw" hreflang="gsw" data-title="Funktion (Mathematik)" data-language-autonym="Alemannisch" data-language-local-name="schweizertyska" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%88%B5%E1%88%A8%E1%8A%AB%E1%89%A2" title="አስረካቢ – amhariska" lang="am" hreflang="am" data-title="አስረካቢ" data-language-autonym="አማርኛ" data-language-local-name="amhariska" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-smn mw-list-item"><a href="https://smn.wikipedia.org/wiki/Funktio" title="Funktio – enaresamiska" lang="smn" hreflang="smn" data-title="Funktio" data-language-autonym="Anarâškielâ" data-language-local-name="enaresamiska" class="interlanguage-link-target"><span>Anarâškielâ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%A7%D9%84%D8%A9" title="دالة – arabiska" lang="ar" hreflang="ar" data-title="دالة" data-language-autonym="العربية" data-language-local-name="arabiska" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Funci%C3%B3n_matematica" title="Función matematica – aragonesiska" lang="an" hreflang="an" data-title="Función matematica" data-language-autonym="Aragonés" data-language-local-name="aragonesiska" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Funci%C3%B3n_matem%C3%A1tica" title="Función matemática – asturiska" lang="ast" hreflang="ast" data-title="Función matemática" data-language-autonym="Asturianu" data-language-local-name="asturiska" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Funksiya_(riyaziyyat)" title="Funksiya (riyaziyyat) – azerbajdzjanska" lang="az" hreflang="az" data-title="Funksiya (riyaziyyat)" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdzjanska" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%AA%E0%A7%87%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%95_(%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4)" title="অপেক্ষক (গণিত) – bengali" lang="bn" hreflang="bn" data-title="অপেক্ষক (গণিত)" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/H%C3%A2m-s%C3%B2%CD%98" title="Hâm-sò͘ – min nan" lang="nan" hreflang="nan" data-title="Hâm-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="min nan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функция (математика) – basjkiriska" lang="ba" hreflang="ba" data-title="Функция (математика)" data-language-autonym="Башҡортса" data-language-local-name="basjkiriska" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%8B%D1%8F_(%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0)" title="Функцыя (матэматыка) – belarusiska" lang="be" hreflang="be" data-title="Функцыя (матэматыка)" data-language-autonym="Беларуская" data-language-local-name="belarusiska" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%8B%D1%8F_(%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0)" title="Функцыя (матэматыка) – belarusiska (tarasjkevitsa)" lang="be-tarask" hreflang="be-tarask" data-title="Функцыя (матэматыка)" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="belarusiska (tarasjkevitsa)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AB%E0%A4%82%E0%A4%95%E0%A5%8D%E0%A4%B6%E0%A4%A8_(%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4)" title="फंक्शन (गणित) – Bhojpuri" lang="bh" hreflang="bh" data-title="फंक्शन (गणित)" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Функция – bulgariska" lang="bg" hreflang="bg" data-title="Функция" data-language-autonym="Български" data-language-local-name="bulgariska" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Funkcija_(matematika)" title="Funkcija (matematika) – bosniska" lang="bs" hreflang="bs" data-title="Funkcija (matematika)" data-language-autonym="Bosanski" data-language-local-name="bosniska" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Funci%C3%B3" title="Funció – katalanska" lang="ca" hreflang="ca" data-title="Funció" data-language-autonym="Català" data-language-local-name="katalanska" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функци (математика) – tjuvasjiska" lang="cv" hreflang="cv" data-title="Функци (математика)" data-language-autonym="Чӑвашла" data-language-local-name="tjuvasjiska" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Funkce_(matematika)" title="Funkce (matematika) – tjeckiska" lang="cs" hreflang="cs" data-title="Funkce (matematika)" data-language-autonym="Čeština" data-language-local-name="tjeckiska" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Murimo_(Masvomhu)" title="Murimo (Masvomhu) – shona" lang="sn" hreflang="sn" data-title="Murimo (Masvomhu)" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Ffwythiant" title="Ffwythiant – walesiska" lang="cy" hreflang="cy" data-title="Ffwythiant" data-language-autonym="Cymraeg" data-language-local-name="walesiska" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Funktion_(matematik)" title="Funktion (matematik) – danska" lang="da" hreflang="da" data-title="Funktion (matematik)" data-language-autonym="Dansk" data-language-local-name="danska" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%AF%D8%A7%D9%84%D8%A9" title="دالة – marockansk arabiska" lang="ary" hreflang="ary" data-title="دالة" data-language-autonym="الدارجة" data-language-local-name="marockansk arabiska" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Funktion_(Mathematik)" title="Funktion (Mathematik) – tyska" lang="de" hreflang="de" data-title="Funktion (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="tyska" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Funktsioon_(matemaatika)" title="Funktsioon (matemaatika) – estniska" lang="et" hreflang="et" data-title="Funktsioon (matemaatika)" data-language-autonym="Eesti" data-language-local-name="estniska" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%85%CE%BD%CE%AC%CF%81%CF%84%CE%B7%CF%83%CE%B7" title="Συνάρτηση – grekiska" lang="el" hreflang="el" data-title="Συνάρτηση" data-language-autonym="Ελληνικά" data-language-local-name="grekiska" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Function_(mathematics)" title="Function (mathematics) – engelska" lang="en" hreflang="en" data-title="Function (mathematics)" data-language-autonym="English" data-language-local-name="engelska" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Funci%C3%B3n_(matem%C3%A1tica)" title="Función (matemática) – spanska" lang="es" hreflang="es" data-title="Función (matemática)" data-language-autonym="Español" data-language-local-name="spanska" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Funkcio_(matematiko)" title="Funkcio (matematiko) – esperanto" lang="eo" hreflang="eo" data-title="Funkcio (matematiko)" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Funtzio_(matematika)" title="Funtzio (matematika) – baskiska" lang="eu" hreflang="eu" data-title="Funtzio (matematika)" data-language-autonym="Euskara" data-language-local-name="baskiska" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%A7%D8%A8%D8%B9" title="تابع – persiska" lang="fa" hreflang="fa" data-title="تابع" data-language-autonym="فارسی" data-language-local-name="persiska" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Function" title="Function – Fiji-hindi" lang="hif" hreflang="hif" data-title="Function" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji-hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Funksj%C3%B3n" title="Funksjón – färöiska" lang="fo" hreflang="fo" data-title="Funksjón" data-language-autonym="Føroyskt" data-language-local-name="färöiska" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Fonction_(math%C3%A9matiques)" title="Fonction (mathématiques) – franska" lang="fr" hreflang="fr" data-title="Fonction (mathématiques)" data-language-autonym="Français" data-language-local-name="franska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Feidhm_(matamaitic)" title="Feidhm (matamaitic) – iriska" lang="ga" hreflang="ga" data-title="Feidhm (matamaitic)" data-language-autonym="Gaeilge" data-language-local-name="iriska" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Funci%C3%B3n" title="Función – galiciska" lang="gl" hreflang="gl" data-title="Función" data-language-autonym="Galego" data-language-local-name="galiciska" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%87%BD%E6%95%B8" title="函數 – gan" lang="gan" hreflang="gan" data-title="函數" data-language-autonym="贛語" data-language-local-name="gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Функция – kalmuckiska" lang="xal" hreflang="xal" data-title="Функция" data-language-autonym="Хальмг" data-language-local-name="kalmuckiska" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%95%A8%EC%88%98" title="함수 – koreanska" lang="ko" hreflang="ko" data-title="함수" data-language-autonym="한국어" data-language-local-name="koreanska" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%96%D5%B8%D6%82%D5%B6%D5%AF%D6%81%D5%AB%D5%A1_(%D5%B4%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1)" title="Ֆունկցիա (մաթեմատիկա) – armeniska" lang="hy" hreflang="hy" data-title="Ֆունկցիա (մաթեմատիկա)" data-language-autonym="Հայերեն" data-language-local-name="armeniska" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AB%E0%A4%B2%E0%A4%A8" title="फलन – hindi" lang="hi" hreflang="hi" data-title="फलन" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Funkcija_(matematika)" title="Funkcija (matematika) – kroatiska" lang="hr" hreflang="hr" data-title="Funkcija (matematika)" data-language-autonym="Hrvatski" data-language-local-name="kroatiska" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Funciono" title="Funciono – ido" lang="io" hreflang="io" data-title="Funciono" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Fungsi_(matematika)" title="Fungsi (matematika) – indonesiska" lang="id" hreflang="id" data-title="Fungsi (matematika)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiska" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Function_(mathematica)" title="Function (mathematica) – interlingua" lang="ia" hreflang="ia" data-title="Function (mathematica)" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Fall_(st%C3%A6r%C3%B0fr%C3%A6%C3%B0i)" title="Fall (stærðfræði) – isländska" lang="is" hreflang="is" data-title="Fall (stærðfræði)" data-language-autonym="Íslenska" data-language-local-name="isländska" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Funzione_(matematica)" title="Funzione (matematica) – italienska" lang="it" hreflang="it" data-title="Funzione (matematica)" data-language-autonym="Italiano" data-language-local-name="italienska" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94" title="פונקציה – hebreiska" lang="he" hreflang="he" data-title="פונקציה" data-language-autonym="עברית" data-language-local-name="hebreiska" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/K%C9%A9lab%C9%A9m" title="Kɩlabɩm – Kabiye" lang="kbp" hreflang="kbp" data-title="Kɩlabɩm" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A4%E1%83%A3%E1%83%9C%E1%83%A5%E1%83%AA%E1%83%98%E1%83%90_(%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%90)" title="ფუნქცია (მათემატიკა) – georgiska" lang="ka" hreflang="ka" data-title="ფუნქცია (მათემატიკა)" data-language-autonym="ქართული" data-language-local-name="georgiska" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функция (математика) – kazakiska" lang="kk" hreflang="kk" data-title="Функция (математика)" data-language-autonym="Қазақша" data-language-local-name="kazakiska" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Fonksyon_(mat%C3%A9matik)" title="Fonksyon (matématik) – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Fonksyon (matématik)" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%95%E0%BA%B3%E0%BA%A5%E0%BA%B2_(%E0%BA%84%E0%BA%B0%E0%BA%99%E0%BA%B4%E0%BA%94%E0%BA%AA%E0%BA%B2%E0%BA%94)" title="ຕຳລາ (ຄະນິດສາດ) – laotiska" lang="lo" hreflang="lo" data-title="ຕຳລາ (ຄະນິດສາດ)" data-language-autonym="ລາວ" data-language-local-name="laotiska" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Functio" title="Functio – latin" lang="la" hreflang="la" data-title="Functio" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Funkcija" title="Funkcija – lettiska" lang="lv" hreflang="lv" data-title="Funkcija" data-language-autonym="Latviešu" data-language-local-name="lettiska" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Funktioun_(Mathematik)" title="Funktioun (Mathematik) – luxemburgiska" lang="lb" hreflang="lb" data-title="Funktioun (Mathematik)" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxemburgiska" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Funkcija_(matematika)" title="Funkcija (matematika) – litauiska" lang="lt" hreflang="lt" data-title="Funkcija (matematika)" data-language-autonym="Lietuvių" data-language-local-name="litauiska" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/fancu" title="fancu – lojban" lang="jbo" hreflang="jbo" data-title="fancu" data-language-autonym="La .lojban." data-language-local-name="lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Fonzion_(matematega)" title="Fonzion (matematega) – lombardiska" lang="lmo" hreflang="lmo" data-title="Fonzion (matematega)" data-language-autonym="Lombard" data-language-local-name="lombardiska" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/F%C3%BCggv%C3%A9ny_(matematika)" title="Függvény (matematika) – ungerska" lang="hu" hreflang="hu" data-title="Függvény (matematika)" data-language-autonym="Magyar" data-language-local-name="ungerska" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функција (математика) – makedonska" lang="mk" hreflang="mk" data-title="Функција (математика)" data-language-autonym="Македонски" data-language-local-name="makedonska" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AB%E0%B4%99%E0%B5%8D%E0%B4%B7%E0%B5%BB" title="ഫങ്ഷൻ – malayalam" lang="ml" hreflang="ml" data-title="ഫങ്ഷൻ" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Funzjonijiet_(matematika)" title="Funzjonijiet (matematika) – maltesiska" lang="mt" hreflang="mt" data-title="Funzjonijiet (matematika)" data-language-autonym="Malti" data-language-local-name="maltesiska" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AB%E0%A4%B2_(%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4)" title="फल (गणित) – marathi" lang="mr" hreflang="mr" data-title="फल (गणित)" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Fungsi" title="Fungsi – malajiska" lang="ms" hreflang="ms" data-title="Fungsi" data-language-autonym="Bahasa Melayu" data-language-local-name="malajiska" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA)" title="Функц (математик) – mongoliska" lang="mn" hreflang="mn" data-title="Функц (математик)" data-language-autonym="Монгол" data-language-local-name="mongoliska" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%96%E1%80%94%E1%80%BA%E1%80%9B%E1%80%BE%E1%80%84%E1%80%BA" title="ဖန်ရှင် – burmesiska" lang="my" hreflang="my" data-title="ဖန်ရှင်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="burmesiska" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Cakacaka_(fika)" title="Cakacaka (fika) – fijianska" lang="fj" hreflang="fj" data-title="Cakacaka (fika)" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fijianska" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Functie_(wiskunde)" title="Functie (wiskunde) – nederländska" lang="nl" hreflang="nl" data-title="Functie (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="nederländska" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%96%A2%E6%95%B0_(%E6%95%B0%E5%AD%A6)" title="関数 (数学) – japanska" lang="ja" hreflang="ja" data-title="関数 (数学)" data-language-autonym="日本語" data-language-local-name="japanska" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Funksion" title="Funksion – nordfrisiska" lang="frr" hreflang="frr" data-title="Funksion" data-language-autonym="Nordfriisk" data-language-local-name="nordfrisiska" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Funksjon_(matematikk)" title="Funksjon (matematikk) – norskt bokmål" lang="nb" hreflang="nb" data-title="Funksjon (matematikk)" data-language-autonym="Norsk bokmål" data-language-local-name="norskt bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Matematisk_funksjon" title="Matematisk funksjon – nynorska" lang="nn" hreflang="nn" data-title="Matematisk funksjon" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorska" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Aplicacion_(matematicas)" title="Aplicacion (matematicas) – occitanska" lang="oc" hreflang="oc" data-title="Aplicacion (matematicas)" data-language-autonym="Occitan" data-language-local-name="occitanska" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Warroomii_(faankishinii)" title="Warroomii (faankishinii) – oromo" lang="om" hreflang="om" data-title="Warroomii (faankishinii)" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Funksiya_(matematika)" title="Funksiya (matematika) – uzbekiska" lang="uz" hreflang="uz" data-title="Funksiya (matematika)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekiska" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AB%E0%A9%B0%E0%A8%95%E0%A8%B8%E0%A8%BC%E0%A8%A8_(%E0%A8%B9%E0%A8%BF%E0%A8%B8%E0%A8%BE%E0%A8%AC)" title="ਫੰਕਸ਼ਨ (ਹਿਸਾਬ) – punjabi" lang="pa" hreflang="pa" data-title="ਫੰਕਸ਼ਨ (ਹਿਸਾਬ)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%81%D9%86%DA%A9%D8%B4%D9%86" title="فنکشن – Western Punjabi" lang="pnb" hreflang="pnb" data-title="فنکشن" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Fongshan_(matimatix)" title="Fongshan (matimatix) – jamaikansk engelsk kreol" lang="jam" hreflang="jam" data-title="Fongshan (matimatix)" data-language-autonym="Patois" data-language-local-name="jamaikansk engelsk kreol" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Fonsion" title="Fonsion – piemontesiska" lang="pms" hreflang="pms" data-title="Fonsion" data-language-autonym="Piemontèis" data-language-local-name="piemontesiska" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Afbillen_(Mathematik)" title="Afbillen (Mathematik) – lågtyska" lang="nds" hreflang="nds" data-title="Afbillen (Mathematik)" data-language-autonym="Plattdüütsch" data-language-local-name="lågtyska" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Funkcja" title="Funkcja – polska" lang="pl" hreflang="pl" data-title="Funkcja" data-language-autonym="Polski" data-language-local-name="polska" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fun%C3%A7%C3%A3o_(matem%C3%A1tica)" title="Função (matemática) – portugisiska" lang="pt" hreflang="pt" data-title="Função (matemática)" data-language-autonym="Português" data-language-local-name="portugisiska" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Func%C8%9Bie" title="Funcție – rumänska" lang="ro" hreflang="ro" data-title="Funcție" data-language-autonym="Română" data-language-local-name="rumänska" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Kinraysuyu" title="Kinraysuyu – quechua" lang="qu" hreflang="qu" data-title="Kinraysuyu" data-language-autonym="Runa Simi" data-language-local-name="quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функция (математика) – ryska" lang="ru" hreflang="ru" data-title="Функция (математика)" data-language-autonym="Русский" data-language-local-name="ryska" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F._%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_%D1%87%D1%8D%D1%80%D1%87%D0%B8%D1%82%D1%8D,_%D1%81%D1%83%D0%BE%D0%BB%D1%82%D0%B0%D0%BB%D0%B0%D1%80%D1%8B%D0%BD_%D1%82%D2%AF%D0%BC%D1%81%D1%8D%D1%8D%D0%BD%D1%8D" title="Функция. Функция чэрчитэ, суолталарын түмсээнэ – jakutiska" lang="sah" hreflang="sah" data-title="Функция. Функция чэрчитэ, суолталарын түмсээнэ" data-language-autonym="Саха тыла" data-language-local-name="jakutiska" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Function_(mathematics)" title="Function (mathematics) – skotska" lang="sco" hreflang="sco" data-title="Function (mathematics)" data-language-autonym="Scots" data-language-local-name="skotska" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Funksioni" title="Funksioni – albanska" lang="sq" hreflang="sq" data-title="Funksioni" data-language-autonym="Shqip" data-language-local-name="albanska" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Funzioni_(matim%C3%A0tica)" title="Funzioni (matimàtica) – sicilianska" lang="scn" hreflang="scn" data-title="Funzioni (matimàtica)" data-language-autonym="Sicilianu" data-language-local-name="sicilianska" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Function_(mathematics)" title="Function (mathematics) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Function (mathematics)" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Zobrazenie_(matematika)" title="Zobrazenie (matematika) – slovakiska" lang="sk" hreflang="sk" data-title="Zobrazenie (matematika)" data-language-autonym="Slovenčina" data-language-local-name="slovakiska" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Funkcija_(matematika)" title="Funkcija (matematika) – slovenska" lang="sl" hreflang="sl" data-title="Funkcija (matematika)" data-language-autonym="Slovenščina" data-language-local-name="slovenska" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Funkcyjo" title="Funkcyjo – silesiska" lang="szl" hreflang="szl" data-title="Funkcyjo" data-language-autonym="Ślůnski" data-language-local-name="silesiska" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Shaqada_(xisaabta)" title="Shaqada (xisaabta) – somaliska" lang="so" hreflang="so" data-title="Shaqada (xisaabta)" data-language-autonym="Soomaaliga" data-language-local-name="somaliska" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%81%D8%A7%D9%86%DA%A9%D8%B4%D9%86_(%D9%85%D8%A7%D8%AA%D9%85%D8%A7%D8%AA%DB%8C%DA%A9)" title="فانکشن (ماتماتیک) – centralkurdiska" lang="ckb" hreflang="ckb" data-title="فانکشن (ماتماتیک)" data-language-autonym="کوردی" data-language-local-name="centralkurdiska" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функција (математика) – serbiska" lang="sr" hreflang="sr" data-title="Функција (математика)" data-language-autonym="Српски / srpski" data-language-local-name="serbiska" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Funkcija" title="Funkcija – serbokroatiska" lang="sh" hreflang="sh" data-title="Funkcija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatiska" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Fungsi_(matematika)" title="Fungsi (matematika) – sundanesiska" lang="su" hreflang="su" data-title="Fungsi (matematika)" data-language-autonym="Sunda" data-language-local-name="sundanesiska" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Funktio" title="Funktio – finska" lang="fi" hreflang="fi" data-title="Funktio" data-language-autonym="Suomi" data-language-local-name="finska" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Punsiyon_(matematika)" title="Punsiyon (matematika) – tagalog" lang="tl" hreflang="tl" data-title="Punsiyon (matematika)" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AE%BE%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AF%81" title="சார்பு – tamil" lang="ta" hreflang="ta" data-title="சார்பு" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tas%C9%A3ent_(tusnakt)" title="Tasɣent (tusnakt) – kabyliska" lang="kab" hreflang="kab" data-title="Tasɣent (tusnakt)" data-language-autonym="Taqbaylit" data-language-local-name="kabyliska" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функция (математика) – tatariska" lang="tt" hreflang="tt" data-title="Функция (математика)" data-language-autonym="Татарча / tatarça" data-language-local-name="tatariska" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9F%E0%B8%B1%E0%B8%87%E0%B8%81%E0%B9%8C%E0%B8%8A%E0%B8%B1%E0%B8%99_(%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C)" title="ฟังก์ชัน (คณิตศาสตร์) – thailändska" lang="th" hreflang="th" data-title="ฟังก์ชัน (คณิตศาสตร์)" data-language-autonym="ไทย" data-language-local-name="thailändska" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Fonksiyon" title="Fonksiyon – turkiska" lang="tr" hreflang="tr" data-title="Fonksiyon" data-language-autonym="Türkçe" data-language-local-name="turkiska" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-udm mw-list-item"><a href="https://udm.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функция (математика) – udmurtiska" lang="udm" hreflang="udm" data-title="Функция (математика)" data-language-autonym="Удмурт" data-language-local-name="udmurtiska" class="interlanguage-link-target"><span>Удмурт</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%96%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функція (математика) – ukrainska" lang="uk" hreflang="uk" data-title="Функція (математика)" data-language-autonym="Українська" data-language-local-name="ukrainska" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AA%D9%81%D8%A7%D8%B9%D9%84_(%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA)" title="تفاعل (ریاضیات) – urdu" lang="ur" hreflang="ur" data-title="تفاعل (ریاضیات)" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D9%81%DB%87%D9%86%D9%83%D8%B3%D9%89%D9%8A%DB%95" title="فۇنكسىيە – uiguriska" lang="ug" hreflang="ug" data-title="فۇنكسىيە" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="uiguriska" class="interlanguage-link-target"><span>ئۇيغۇرچە / Uyghurche</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Funkcii_(matematik)" title="Funkcii (matematik) – veps" lang="vep" hreflang="vep" data-title="Funkcii (matematik)" data-language-autonym="Vepsän kel’" data-language-local-name="veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%A0m_s%E1%BB%91" title="Hàm số – vietnamesiska" lang="vi" hreflang="vi" data-title="Hàm số" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesiska" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%98%A0%E5%B0%84" title="映射 – litterär kineiska" lang="lzh" hreflang="lzh" data-title="映射" data-language-autonym="文言" data-language-local-name="litterär kineiska" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Funsiyon_(matematika)" title="Funsiyon (matematika) – waray" lang="war" hreflang="war" data-title="Funsiyon (matematika)" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%87%BD%E6%95%B0" title="函数 – wu" lang="wuu" hreflang="wuu" data-title="函数" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%A2" title="פונקציע – jiddisch" lang="yi" hreflang="yi" data-title="פונקציע" data-language-autonym="ייִדיש" data-language-local-name="jiddisch" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%87%BD%E6%95%B8" title="函數 – kantonesiska" lang="yue" hreflang="yue" data-title="函數" data-language-autonym="粵語" data-language-local-name="kantonesiska" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Funkc%C4%97j%C4%97" title="Funkcėjė – samogitiska" lang="sgs" hreflang="sgs" data-title="Funkcėjė" data-language-autonym="Žemaitėška" data-language-local-name="samogitiska" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%87%BD%E6%95%B0" title="函数 – kinesiska" lang="zh" hreflang="zh" data-title="函数" data-language-autonym="中文" data-language-local-name="kinesiska" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B5%9C%E2%B4%B0%E2%B5%99%E2%B5%96%E2%B5%8F%E2%B5%9C_(%E2%B5%9C%E2%B5%93%E2%B5%99%E2%B5%8F%E2%B4%B0%E2%B4%BD%E2%B5%9C)" title="ⵜⴰⵙⵖⵏⵜ (ⵜⵓⵙⵏⴰⴽⵜ) – marockansk standard-tamazight" lang="zgh" hreflang="zgh" data-title="ⵜⴰⵙⵖⵏⵜ (ⵜⵓⵙⵏⴰⴽⵜ)" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="marockansk standard-tamazight" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11348#sitelinks-wikipedia" title="Redigera interwikilänkar" class="wbc-editpage">Redigera länkar</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div 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Wikipedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sv" dir="ltr"><div class="noexcerpt noprint hanvisning_bas"> <dl><dd><i>Uppslagsordet ”f(x)” leder hit.  För den sydkoreanska musikgruppen, se <a href="/wiki/F(x)_(musikgrupp)" title="F(x) (musikgrupp)">f(x) (musikgrupp)</a>.  För andra betydelser, se <a href="/wiki/Funktion_(olika_betydelser)" class="mw-disambig" title="Funktion (olika betydelser)">Funktion (olika betydelser)</a>.</i></dd></dl></div> <table style="border: 1px solid #aaaaaa; background-color: #f9f9f9; color: black; margin-bottom: 0.5em; margin-left: 1em; padding: .2em; float: right; clear: right;"> <tbody><tr> <th style="background:#ccccff;"><a href="/wiki/Matematik" title="Matematik">Matematiska begrepp</a> </th></tr> <tr> <td> <ul><li><a href="/wiki/Tal_(matematik)" class="mw-redirect" title="Tal (matematik)">Tal</a></li> <li><a href="/wiki/M%C3%A4ngd" title="Mängd">Mängd</a></li> <li><a href="/wiki/Variabel" title="Variabel">Variabel</a></li> <li><a href="/wiki/Ekvation" title="Ekvation">Ekvation</a></li> <li><a class="mw-selflink selflink">Funktion</a></li> <li><a href="/wiki/Operator" title="Operator">Operator</a></li> <li><a href="/wiki/Vektor_(matematik)" class="mw-redirect" title="Vektor (matematik)">Vektor</a></li> <li><a href="/wiki/Linj%C3%A4rt_rum" title="Linjärt rum">Linjärt rum</a></li></ul> </td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Function_machine2-sv.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Function_machine2-sv.svg/250px-Function_machine2-sv.svg.png" decoding="async" width="250" height="247" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Function_machine2-sv.svg/375px-Function_machine2-sv.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Function_machine2-sv.svg/500px-Function_machine2-sv.svg.png 2x" data-file-width="191" data-file-height="189" /></a><figcaption>En funktion <i>f</i> tar ett invärde <i>x</i>, och returnerar ett utvärde <i>f(x)</i>. En liknelse är att beskriva funktionen som en maskin eller hemlig låda som för vissa invärden returnerar bestämda utvärden.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Cubicpoly.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Cubicpoly.svg/250px-Cubicpoly.svg.png" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Cubicpoly.svg/375px-Cubicpoly.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Cubicpoly.svg/500px-Cubicpoly.svg.png 2x" data-file-width="1000" data-file-height="1000" /></a><figcaption>En funktion kan åskådliggöras i en <a href="/wiki/Linjediagram" title="Linjediagram">graf</a>. Detta är funktionen <i>f</i>(<i>x</i>) = <i>x</i><sup>3</sup> − 9<i>x</i>. </figcaption></figure> <p>En <b>funktion</b> inom <a href="/wiki/Matematik" title="Matematik">matematiken</a> är en regel som till varje <i>invärde</i> kopplar <i>utvärden</i>. Ofta beskrivs sambandet mellan invärde och utvärde med en matematisk formel, där invärdet representeras med en eller flera <a href="/wiki/Variabel" title="Variabel">variabler</a>, alternativt med en tabell eller grafiskt med en <a href="/wiki/Linjediagram" title="Linjediagram">graf</a>, ett <a href="/wiki/Sambandsdiagram" title="Sambandsdiagram">sambandsdiagram</a> eller ett pildiagram. En viktig egenskap hos funktioner är att de är deterministiska (det vill säga konsekventa, så att varje invärde alltid ger samma utvärde). Detta gör att funktionen kan ses som en maskin, som systematiskt levererar utvärden så fort man stoppar in invärden. </p><p>Invärdet <i>x</i> till funktionen <i>f</i> kallas inom <a href="/wiki/Matematisk_analys" title="Matematisk analys">matematisk analys</a> ofta ’’invariabel’’ och inom <a href="/wiki/Numerisk_analys" title="Numerisk analys">beräkningsvetenskap</a> för ’’funktionsargument’’ eller ’’argument’’. Det resulterande utvärdet <i>f</i>(<i>x</i>) kallas ’’funktionsvärdet’’ eller ’’<a href="/wiki/V%C3%A4rde_(matematik)" title="Värde (matematik)">värdet</a>’’. </p><p>En funktion som är vanligt förekommande som byggsten i matematiska formler kallas <a href="/wiki/Element%C3%A4r_funktion" title="Elementär funktion">elementär funktion</a>, och har ett specifikt namn såsom <a href="/wiki/Sinus" title="Sinus">sinusfunktion</a>, <a href="/wiki/Kvadratrot" title="Kvadratrot">kvadratrot</a> eller <a href="/wiki/Logaritm" title="Logaritm">logaritm</a>. En <a href="/wiki/Funktionsr%C3%A4knare" title="Funktionsräknare">funktionsräknare</a> (en vetenskaplig kalkylator) är en miniräknare som kan beräkna värdet av elementära funktioner. En <a href="/wiki/Grafritande_minir%C3%A4knare" title="Grafritande miniräknare">grafritande miniräknare</a> kan visa grafer för funktionsuttryck. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etymologi">Etymologi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funktion&veaction=edit&section=1" title="Redigera avsnitt: Etymologi" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funktion&action=edit&section=1" title="Redigera avsnitts källkod: Etymologi"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ordet funktion kommer av <a href="/wiki/Latin" title="Latin">latinets</a> <i>functio</i> som betyder "fullgörande, verkställande", det vill säga att någonting görs färdigt, att någonting fixas.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-reference-link-bracket">[</span>1<span class="cite-reference-link-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Intuitiv_introduktion">Intuitiv introduktion</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funktion&veaction=edit&section=2" title="Redigera avsnitt: Intuitiv introduktion" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funktion&action=edit&section=2" title="Redigera avsnitts källkod: Intuitiv introduktion"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En funktion är en regel eller procedur som tillordnar ett utvärde för varje givet invärde.<sup id="cite_ref-böiers_2-0" class="reference"><a href="#cite_note-böiers-2"><span class="cite-reference-link-bracket">[</span>2<span class="cite-reference-link-bracket">]</span></a></sup> Följande är exempel på funktioner: </p> <ul><li>I en grupp människor har varje person en favoritfärg bland färgerna röd, orange, gul, grön, blå, indigo och violett. Invärdet till funktionen är i detta fall en person, och utvärdet är en av de sju färgerna. Favoritfärgen är en funktion av person till färg. Johan kan till exempel ha favoritfärgen röd, medan Kent har favoritfärgen violett. Det är fullt möjligt för två personer att ha samma favoritfärg. Det kan till exempel vara så att både Anna och Johan tycker om rött.</li></ul> <ul><li>En sten som släpps från olika våningsplan i en hög byggnad får olika falltid. Det kan till exempel ta 2 sekunder att falla från den 2:a våningen och 4 sekunder från den 8:e. Här är våningsplansnumret invärde och utvärdet är den tid som det tar för stenen att nå fram till markplanet.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funktion&veaction=edit&section=3" title="Redigera avsnitt: Definition" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funktion&action=edit&section=3" title="Redigera avsnitts källkod: Definition"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Injection_keine_Injektion_2a.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Injection_keine_Injektion_2a.svg/250px-Injection_keine_Injektion_2a.svg.png" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Injection_keine_Injektion_2a.svg/375px-Injection_keine_Injektion_2a.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Injection_keine_Injektion_2a.svg/500px-Injection_keine_Injektion_2a.svg.png 2x" data-file-width="200" data-file-height="200" /></a><figcaption>I pildiagrammet ovan är elementen i mängden Y en <a href="/wiki/Diskret_funktion" title="Diskret funktion">diskret funktion</a> av elementen i mängden X, eftersom varje element i X är associerat till ett och endast ett element i Y, det vill säga avbildningen är <a href="/wiki/Injektiv_funktion" title="Injektiv funktion">injektiv</a>. Funktionen kan beskrivas som en uppsättning av ordnade par {(1, D), (2, C), (3, C)}. X kallas funktionens <a href="/wiki/Definitionsm%C3%A4ngd" title="Definitionsmängd">definitionsmängd</a>, Y dess <a href="/wiki/M%C3%A5lm%C3%A4ngd" title="Målmängd">målmängd</a>, och elementen {D, C} dess <a href="/wiki/V%C3%A4rdem%C3%A4ngd" title="Värdemängd">värdemängd</a>. Funktionen i detta exempel är inte <a href="/wiki/Surjektiv_funktion" title="Surjektiv funktion">surjektiv</a> och <a href="/wiki/Bijektiv_funktion" title="Bijektiv funktion">bijektiv</a> och saknar således funktionsinvers, det vill säga elementen i X är inte en funktion av elementen i Y, eftersom varje element i Y inte är associerat till ett element i X.</figcaption></figure> <p>Låt A och B vara två <a href="/wiki/M%C3%A4ngd" title="Mängd">mängder</a>, där ingen av dem är <a href="/wiki/Tomma_m%C3%A4ngden" title="Tomma mängden">tom</a>. En funktion <i>f</i> från A till B är en <a href="/wiki/Avbildning" title="Avbildning">avbildning</a> från A till B som definierar exakt ett element i B till varje element i A, vilket formellt skrivs <i>f:A → B</i>.<sup id="cite_ref-durbin_3-0" class="reference"><a href="#cite_note-durbin-3"><span class="cite-reference-link-bracket">[</span>3<span class="cite-reference-link-bracket">]</span></a></sup> </p><p>Normalt skriver man dock <i>f</i>(a)=b där b är det unika elementet i B som <i>f</i> tillordnar elementet a i A. Om det finns <i>minst ett</i> element a för varje element i B kallas funktionen <a href="/wiki/Surjektiv_funktion" title="Surjektiv funktion">surjektiv</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-reference-link-bracket">[</span>4<span class="cite-reference-link-bracket">]</span></a></sup> Om det för varje element i B finns <i>som mest</i> ett element a kallas funktionen <a href="/wiki/Injektiv_funktion" title="Injektiv funktion">injektiv</a>. En funktion som är både injektiv och surjektiv – det vill säga det finns ett och endast ett element a för varje element i B – kallas <a href="/wiki/Bijektiv_funktion" title="Bijektiv funktion">bijektiv</a>. Bijektiva funktioner är intressanta då de har en <a href="/wiki/Invers_funktion" title="Invers funktion">invers</a>. </p><p>En typ av funktion som ofta diskuteras har matematiska tal både som invärde och som utvärde och fungerar så att utvärdet uttrycks som en formel där (det obestämda) invärdet ingår. Utvärdet beräknas då genom att man först ersätter symbolen för invärdet med ett visst invärde som man är intresserad av. Därefter kan man beräkna ett utvärde för detta invärde genom att räkna ut värdet av den formel som nu innehåller endast kända matematiska tal. </p><p>Tänk till exempel på formeln </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84ddac4ae10b1aa4a11741c79771a583419fb1fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.9ex; height:3.176ex;" alt="{\displaystyle f(x)=x^{2}}"></span></dd></dl> <p>som för varje tal <i>x</i> tillordnar detta tal ett associerat värde, <i>x</i> i kvadrat. </p><p>En naturlig generalisering är att låta funktionen bero av flera invärden.<sup id="cite_ref-böiers_2-1" class="reference"><a href="#cite_note-böiers-2"><span class="cite-reference-link-bracket">[</span>2<span class="cite-reference-link-bracket">]</span></a></sup> Som exempel är </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g(x,y)=xy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(x,y)=xy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9435861e2e572f5ce266e70f0fcc0cf83f9d1b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.028ex; height:2.843ex;" alt="{\displaystyle g(x,y)=xy}"></span></dd></dl> <p>en funktion som tar två värden, <i>x</i> och <i>y</i>, och tillordnar dem ett utvärde som är produkten av dem, <i>x . y</i>. Man kan kanske tycka att den här regeln inte stämmer på beskrivningen ovan, eftersom den kräver två invärden. Dock är det fullt möjligt att se varje sådant par av värden som ett enda värde, i vid bemärkelse. Sådana värden kallas ordnade par, (<i>x</i>, <i>y</i>). </p><p>I <a href="/wiki/Naturvetenskap" title="Naturvetenskap">naturvetenskap</a> stöter man ofta på funktioner som inte kan definieras med hjälp av en känd formel. (Det vill säga att man inte känner till någon formel, även om det kanske finns en.) Ett exempel på detta är <a href="/wiki/Jorden" title="Jorden">jordytans</a> temperatur över tiden. Den är en funktion som har plats (två <a href="/wiki/Geografiska_koordinatsystem" title="Geografiska koordinatsystem">koordinater</a>) och tid som invärde och ger ett utvärde som är en temperatur. </p><p>Det intuitiva funktionsbegreppet är alltså inte begränsat till beräkningar från enstaka tal och inte ens begränsat till beräkningar. Det matematiska funktionsbegreppet är ännu mer generellt (obegränsat) och inte alls begränsat till att handla om matematiska tal. Detta gör att funktionsbegreppet är en grundsten i nästan varje gren av matematiken och naturvetenskapen. </p><p>Om en variabel <i>y</i> definieras som funktionsvärdet, det vill säga </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2311a6a75c54b0ea085a381ba472c31d59321514" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.672ex; height:2.843ex;" alt="{\displaystyle y=f(x)}"></span>,</dd></dl> <p>kallas <i>y</i> för <a href="/wiki/Beroende_variabel" title="Beroende variabel">beroende variabel</a>, medan <i>x</i> är <a href="/wiki/Oberoende_variabel" title="Oberoende variabel">oberoende variabel</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Formell_definition">Formell definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funktion&veaction=edit&section=4" title="Redigera avsnitt: Formell definition" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funktion&action=edit&section=4" title="Redigera avsnitts källkod: Formell definition"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En funktion<sup id="cite_ref-durbin_3-1" class="reference"><a href="#cite_note-durbin-3"><span class="cite-reference-link-bracket">[</span>3<span class="cite-reference-link-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:X\to Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:X\to Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abd1e080abef4bbdab67b43819c6431e7561361c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.583ex; height:2.509ex;" alt="{\displaystyle f:X\to Y}"></span></dd></dl> <p>är en <a href="/wiki/Bin%C3%A4r_relation" title="Binär relation">binär relation</a> <i>R</i> på <i>X</i> × <i>Y</i> sådan att </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall x\in X\ \exists y\in Y(R(x,y)\land \forall z\in Y(R(x,z)\rightarrow z=y))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>∈</mo> <mi>X</mi> <mtext> </mtext> <mi mathvariant="normal">∃</mi> <mi>y</mi> <mo>∈</mo> <mi>Y</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi mathvariant="normal">∀</mi> <mi>z</mi> <mo>∈</mo> <mi>Y</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mi>z</mi> <mo>=</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x\in X\ \exists y\in Y(R(x,y)\land \forall z\in Y(R(x,z)\rightarrow z=y))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38fdbb4134436f83262c84c29fac090670de785a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:51.355ex; height:2.843ex;" alt="{\displaystyle \forall x\in X\ \exists y\in Y(R(x,y)\land \forall z\in Y(R(x,z)\rightarrow z=y))}"></span></dd></dl> <p>En vanlig beteckning är då </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a5080a8b0a963407ea74ffa50702563771518d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.672ex; height:2.843ex;" alt="{\displaystyle f(x)=y}"></span></dd></dl> <p>Om vi frångår ovanstående villkor heter det att funktionen är <i>flervärd</i>. Detta är fallet för många komplexa funktioner, till exempel komplexa logaritm- och argumentfunktionerna och komplex exponentiering med godtycklig bas. Ofta definierar man då en ny funktion som inte är flervärd, och använder den kanoniska <i>principalgrenen</i> av värdena för ett argument. Principalvarianten av en flervärd funktion brukar betecknas med versal i början, till exempel </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Log} ,\,\mathrm {Arg} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">g</mi> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">g</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Log} ,\,\mathrm {Arg} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30f9517252190a92bb3372fd4cb51a02c0ece655" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.016ex; height:2.509ex;" alt="{\displaystyle \mathrm {Log} ,\,\mathrm {Arg} }"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Exempel_på_funktioner"><span id="Exempel_p.C3.A5_funktioner"></span>Exempel på funktioner</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funktion&veaction=edit&section=5" title="Redigera avsnitt: Exempel på funktioner" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funktion&action=edit&section=5" title="Redigera avsnitts källkod: Exempel på funktioner"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Linj%C3%A4r_funktion" title="Linjär funktion">Linjär funktion</a></li> <li><a href="/wiki/Polynom" title="Polynom">Polynomfunktion</a></li> <li><a href="/wiki/Exponentialfunktion" title="Exponentialfunktion">Exponentialfunktion</a></li> <li><a href="/wiki/Trigonometrisk_funktion" title="Trigonometrisk funktion">Trigonometrisk funktion</a></li> <li><a href="/wiki/Hyperbolisk_funktion" title="Hyperbolisk funktion">Hyperbolisk funktion</a></li> <li><a href="/wiki/Gammafunktionen" title="Gammafunktionen">Gammafunktionen</a></li> <li><a href="/wiki/Betafunktionen" title="Betafunktionen">Betafunktionen</a></li> <li><a href="/wiki/Matrisfunktion" title="Matrisfunktion">Matrisfunktion</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Typer_av_funktioner">Typer av funktioner</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funktion&veaction=edit&section=6" title="Redigera avsnitt: Typer av funktioner" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funktion&action=edit&section=6" title="Redigera avsnitts källkod: Typer av funktioner"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Element%C3%A4r_funktion" title="Elementär funktion">Elementär funktion</a></li> <li><a href="/wiki/Kontinuerlig_funktion" title="Kontinuerlig funktion">Kontinuerlig funktion</a></li> <li><a href="/wiki/Glatt_funktion" title="Glatt funktion">Glatt funktion</a></li> <li><a href="/wiki/Analytisk_funktion" title="Analytisk funktion">Analytisk funktion</a></li> <li><a href="/wiki/Implicit_funktion" title="Implicit funktion">Implicit funktion</a></li> <li><a href="/wiki/Invers_funktion" title="Invers funktion">Invers funktion</a></li> <li><a href="/wiki/Sammansatt_funktion" title="Sammansatt funktion">Sammansatt funktion</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Se_även"><span id="Se_.C3.A4ven"></span>Se även</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funktion&veaction=edit&section=7" title="Redigera avsnitt: Se även" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funktion&action=edit&section=7" title="Redigera avsnitts källkod: Se även"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Lista_%C3%B6ver_funktioner" class="mw-redirect" title="Lista över funktioner">Lista över funktioner</a></li> <li><a href="/wiki/Derivata" title="Derivata">Derivata</a></li> <li><a href="/wiki/Integral" title="Integral">Integral</a></li> <li><a href="/wiki/Transformation_(matematik)" title="Transformation (matematik)">Transformation</a></li> <li><a href="/wiki/Avbildning" title="Avbildning">Avbildning</a></li> <li><a href="/wiki/Operator" title="Operator">Operator</a></li> <li><a href="/wiki/Distribution" title="Distribution">Distribution</a></li> <li><a href="/wiki/Injektiv_funktion" title="Injektiv funktion">Injektiv funktion</a></li> <li><a href="/wiki/Surjektiv_funktion" title="Surjektiv funktion">Surjektiv funktion</a></li> <li><a href="/wiki/Bijektiv_funktion" title="Bijektiv funktion">Bijektiv funktion</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Källor"><span id="K.C3.A4llor"></span>Källor</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funktion&veaction=edit&section=8" title="Redigera avsnitt: Källor" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funktion&action=edit&section=8" title="Redigera avsnitts källkod: Källor"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <span class="reference-text"><i>Svenska akademiens ordbok</i>, Funktion (Hämtad 11 maj 2013)</span> </li> <li id="cite_note-böiers-2">^ [<a href="#cite_ref-böiers_2-0"><small>a</small></a> <a href="#cite_ref-böiers_2-1"><small>b</small></a>] <span class="reference-text"><cite style="font-style:normal" class="book" id="CITEREFBöiers,_Persson2009">Böiers, Persson (2009). <i><span>Analys i flera variabler</span></i>. sid. 1. <a href="/wiki/Special:Bokk%C3%A4llor/91-44-03869-0" title="Special:Bokkällor/91-44-03869-0">ISBN 91-44-03869-0</a></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Analys+i+flera+variabler&rft.aulast=B%C3%B6iers%2C+Persson&rft.au=B%C3%B6iers%2C+Persson&rft.date=2009&rft.pages=sid.%26nbsp%3B1&rft.isbn=91-44-03869-0&rfr_id=info:sid/en.wikipedia.org:Funktion"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-durbin-3">^ [<a href="#cite_ref-durbin_3-0"><small>a</small></a> <a href="#cite_ref-durbin_3-1"><small>b</small></a>] <span class="reference-text"><cite style="font-style:normal" class="book" id="CITEREFDurbin2005">Durbin, J (2005). <i><span>Modern Algebra</span></i>. sid. 9. <a href="/wiki/Special:Bokk%C3%A4llor/0-471-43335-7" title="Special:Bokkällor/0-471-43335-7">ISBN 0-471-43335-7</a></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modern+Algebra&rft.aulast=Durbin&rft.aufirst=J&rft.au=Durbin%2C+J&rft.date=2005&rft.pages=sid.%26nbsp%3B9&rft.isbn=0-471-43335-7&rfr_id=info:sid/en.wikipedia.org:Funktion"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-4"><a href="#cite_ref-4">^</a> <span class="reference-text"><cite style="font-style:normal" class="book" id="CITEREFBöiers,_Persson2009">Böiers, Persson (2009). <i><span>Analys i flera variabler</span></i>. sid. 412. <a href="/wiki/Special:Bokk%C3%A4llor/91-44-03869-0" title="Special:Bokkällor/91-44-03869-0">ISBN 91-44-03869-0</a></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Analys+i+flera+variabler&rft.aulast=B%C3%B6iers%2C+Persson&rft.au=B%C3%B6iers%2C+Persson&rft.date=2009&rft.pages=sid.%26nbsp%3B412&rft.isbn=91-44-03869-0&rfr_id=info:sid/en.wikipedia.org:Funktion"><span style="display: none;"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Externa_länkar"><span id="Externa_l.C3.A4nkar"></span>Externa länkar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funktion&veaction=edit&section=9" title="Redigera avsnitt: Externa länkar" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funktion&action=edit&section=9" title="Redigera avsnitts källkod: Externa länkar"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> Wikimedia Commons har media som rör <a href="https://commons.wikimedia.org/wiki/Category:Functions_(mathematics)" class="extiw" title="commons:Category:Functions (mathematics)">funktion</a>.</li></ul> <p><br /> </p> <style data-mw-deduplicate="TemplateStyles:r56287950">.mw-parser-output table.navbox{border:#aaa 1px solid;width:100%;margin:auto;margin-top:1em;clear:both;font-size:88%;text-align:center;padding:1px}.mw-parser-output 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