{"id":372,"date":"2023-07-04T07:39:56","date_gmt":"2023-07-04T07:39:56","guid":{"rendered":"https:\/\/mathority.org\/pt\/funcao-de-identidade\/"},"modified":"2023-07-04T07:39:56","modified_gmt":"2023-07-04T07:39:56","slug":"funcao-de-identidade","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/funcao-de-identidade\/","title":{"rendered":"Fun\u00e7\u00e3o de identidade"},"content":{"rendered":"<p>Aqui voc\u00ea descobrir\u00e1 o que \u00e9 a fun\u00e7\u00e3o identidade. Al\u00e9m disso, voc\u00ea poder\u00e1 ver como representar graficamente a fun\u00e7\u00e3o identidade e quais s\u00e3o suas caracter\u00edsticas. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-identidad\"><\/span> O que \u00e9 uma fun\u00e7\u00e3o de identidade?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Uma fun\u00e7\u00e3o identidade \u00e9 aquela fun\u00e7\u00e3o que tem como imagem o mesmo valor do argumento.<\/strong> A fun\u00e7\u00e3o identidade pode ser expressa com o termo <em><strong>id<\/strong><\/em> .<\/p>\n<p> Portanto, a express\u00e3o matem\u00e1tica para a fun\u00e7\u00e3o identidade \u00e9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-983fed5b7a164bfcb0d3e0b5cebfd4c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"68\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Por exemplo, a imagem da fun\u00e7\u00e3o identidade para x=1 vale 1, a imagem de x=2 vale 2, a imagem de x=3 vale 3,\u2026<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b85e48e3f36d1eb4271b265aaf35bef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(1)=1\\\\[2ex]f(2)=2\\\\[2ex]f(3)=3\\\\ \\bm{\\vdots}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"120\" width=\"66\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> A fun\u00e7\u00e3o identidade \u00e9 um exemplo de fun\u00e7\u00e3o linear. No link a seguir voc\u00ea pode ver mais exemplos deste tipo de fun\u00e7\u00f5es:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/funcao-linear-e-afim\/\">exemplos de fun\u00e7\u00f5es lineares<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"representacion-grafica-de-la-funcion-identidad\"><\/span> Representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o identidade<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O gr\u00e1fico da fun\u00e7\u00e3o identidade corresponde a uma reta que \u00e9 a bissetriz do primeiro e terceiro quadrantes. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fonction-didentite.webp\" alt=\"fun\u00e7\u00e3o de identidade\" class=\"wp-image-616\" width=\"404\" height=\"403\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Como voc\u00ea pode ver, a fun\u00e7\u00e3o identidade passa pela origem das coordenadas (ponto (0,0)) e tem inclina\u00e7\u00e3o igual \u00e0 unidade (m=1), pois uma unidade da vari\u00e1vel aumenta e para cada valor do independente vari\u00e1vel X. Al\u00e9m disso, a fun\u00e7\u00e3o identidade forma um \u00e2ngulo de 45\u00ba com o eixo X. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-funcion-identidad\"><\/span> Caracter\u00edsticas da fun\u00e7\u00e3o identidade<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A fun\u00e7\u00e3o identidade possui as seguintes propriedades:<\/p>\n<ul>\n<li> O dom\u00ednio da fun\u00e7\u00e3o identidade s\u00e3o todos os n\u00fameros reais:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f6a5bb1d7547a2d733c138cfc33c6f3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f=\\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul>\n<li> O contradom\u00ednio (ou contradom\u00ednio) da fun\u00e7\u00e3o identidade tamb\u00e9m consiste em todos os n\u00fameros reais:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a3ecde093819f7093a822146403ef191_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Im } f=\\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul>\n<li> A fun\u00e7\u00e3o identidade \u00e9 uma fun\u00e7\u00e3o cont\u00ednua e bijetiva.<\/li>\n<\/ul>\n<ul>\n<li> Al\u00e9m disso, a fun\u00e7\u00e3o identidade consiste em uma fun\u00e7\u00e3o \u00edmpar, o que significa que \u00e9 uma fun\u00e7\u00e3o sim\u00e9trica em rela\u00e7\u00e3o \u00e0 origem das coordenadas.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5db584bb9d529c83c3c80bb43b4c96c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(-x)=-f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"119\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/simetria-de-uma-funcao-simetrica-e-assimetrica\/\">fun\u00e7\u00e3o sim\u00e9trica \u00edmpar<\/a><\/span><\/p>\n<ul>\n<li> A fun\u00e7\u00e3o identidade \u00e9 crescente em todo o seu dom\u00ednio e sua inclina\u00e7\u00e3o \u00e9 igual a 1.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d94dded0dc9c883f82d566d62e2d4b42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Intersecta o eixo x (eixo OX) e o eixo y (eixo Y) no mesmo ponto: a origem da coordenada.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9cf2000c782cfe94be6df5f499cd3e24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Pode ser classificada como uma fun\u00e7\u00e3o polinomial de primeiro grau.<\/li>\n<\/ul>\n<ul>\n<li> A fun\u00e7\u00e3o identidade atua como um elemento neutro da <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/composicao-de-funcoes-funcao-composta\/\">composi\u00e7\u00e3o da fun\u00e7\u00e3o<\/a><\/span> . Para que qualquer fun\u00e7\u00e3o composta com a fun\u00e7\u00e3o identidade resulte na pr\u00f3pria fun\u00e7\u00e3o.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-492b02c1d4c5597bb42d3378c7f2d4aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\circ id =id \\circ f=f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"143\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul>\n<li> O valor que\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a \u00fanica raiz deste tipo de fun\u00e7\u00e3o.<\/li>\n<\/ul>\n<ul>\n<li> O limite da fun\u00e7\u00e3o identidade quando x tende para mais infinito ou menos infinito d\u00e1 respectivamente mais infinito e menos infinito:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1459a4b1c6280a67227c0a432d4bd0ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty} f(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"138\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-84deabbc661b9768d7dfe27dee84ca99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to -\\infty} f(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"138\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> A fun\u00e7\u00e3o identidade, portanto, n\u00e3o tem ass\u00edntota.<\/li>\n<\/ul>\n<ul>\n<li> A derivada da fun\u00e7\u00e3o identidade \u00e9 a fun\u00e7\u00e3o constante com valor 1:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a90dcf49bd1389d625f48fc4770eff1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x \\ \\longrightarrow \\ f'(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"189\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> A integral da fun\u00e7\u00e3o identidade \u00e9 a fun\u00e7\u00e3o quadr\u00e1tica:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60083c016c4d5015ce7dc59e2e864c3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\int x \\ dx= \\frac{x^2}{2} + C\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"137\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/funcao-de-parabola-quadratica\/\">f\u00f3rmula da fun\u00e7\u00e3o quadr\u00e1tica<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aqui voc\u00ea descobrir\u00e1 o que \u00e9 a fun\u00e7\u00e3o identidade. Al\u00e9m disso, voc\u00ea poder\u00e1 ver como representar graficamente a fun\u00e7\u00e3o identidade e quais s\u00e3o suas caracter\u00edsticas. O que \u00e9 uma fun\u00e7\u00e3o de identidade? Uma fun\u00e7\u00e3o identidade \u00e9 aquela fun\u00e7\u00e3o que tem como imagem o mesmo valor do argumento. A fun\u00e7\u00e3o identidade pode ser expressa com o &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/funcao-de-identidade\/\"> <span class=\"screen-reader-text\">Fun\u00e7\u00e3o de identidade<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[22],"tags":[],"class_list":["post-372","post","type-post","status-publish","format-standard","hentry","category-representacao-de-funcao"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Fun\u00e7\u00e3o Identidade - Matoridade<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/funcao-de-identidade\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fun\u00e7\u00e3o Identidade - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea descobrir\u00e1 o que \u00e9 a fun\u00e7\u00e3o identidade. 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Al\u00e9m disso, voc\u00ea poder\u00e1 ver como representar graficamente a fun\u00e7\u00e3o identidade e quais s\u00e3o suas caracter\u00edsticas. O que \u00e9 uma fun\u00e7\u00e3o de identidade? Uma fun\u00e7\u00e3o identidade \u00e9 aquela fun\u00e7\u00e3o que tem como imagem o mesmo valor do argumento. 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