{"id":371,"date":"2023-07-04T08:20:07","date_gmt":"2023-07-04T08:20:07","guid":{"rendered":"https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/"},"modified":"2023-07-04T08:20:07","modified_gmt":"2023-07-04T08:20:07","slug":"funcoes-nao-lineares","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/","title":{"rendered":"Fun\u00e7\u00f5es n\u00e3o lineares"},"content":{"rendered":"

Neste artigo, voc\u00ea aprender\u00e1 o que s\u00e3o fun\u00e7\u00f5es n\u00e3o lineares. Tamb\u00e9m explicamos as diferen\u00e7as entre fun\u00e7\u00f5es lineares e fun\u00e7\u00f5es n\u00e3o lineares. E, al\u00e9m disso, voc\u00ea poder\u00e1 ver quais s\u00e3o os diferentes tipos de fun\u00e7\u00f5es n\u00e3o lineares com exemplos. <\/p>\n

<\/span> O que \u00e9 uma fun\u00e7\u00e3o n\u00e3o linear?<\/span><\/h2>\n

Uma fun\u00e7\u00e3o n\u00e3o linear \u00e9 uma fun\u00e7\u00e3o cuja representa\u00e7\u00e3o gr\u00e1fica n\u00e3o \u00e9 uma linha reta, mas sim outra forma.<\/strong><\/p>\n

Portanto, fun\u00e7\u00f5es polinomiais<\/a><\/span> de primeiro grau s\u00e3o as \u00fanicas que n\u00e3o s\u00e3o fun\u00e7\u00f5es n\u00e3o lineares. <\/p>\n

<\/span> Quais s\u00e3o as diferen\u00e7as entre uma fun\u00e7\u00e3o linear e uma fun\u00e7\u00e3o n\u00e3o linear?<\/span><\/h2>\n

A principal diferen\u00e7a entre uma fun\u00e7\u00e3o linear e uma fun\u00e7\u00e3o n\u00e3o linear \u00e9 a sua representa\u00e7\u00e3o gr\u00e1fica<\/strong> , pois os gr\u00e1ficos de todas as fun\u00e7\u00f5es lineares s\u00e3o retas, por outro lado, os gr\u00e1ficos das fun\u00e7\u00f5es n\u00e3o lineares podem ter qualquer formato: par\u00e1bolas, curvas c\u00fabicas, hip\u00e9rboles etc.<\/p>\n

Abaixo voc\u00ea pode ver uma fun\u00e7\u00e3o n\u00e3o linear e uma fun\u00e7\u00e3o linear representada graficamente: <\/p>\n

\n
\n

fun\u00e7\u00e3o n\u00e3o linear<\/strong> <\/p>\n

\n
\"\"<\/figure>\n<\/div>\n<\/div>\n
\n

Fun\u00e7\u00e3o linear<\/strong> <\/p>\n

\n
\"\"<\/figure>\n<\/div>\n<\/div>\n<\/div>\n

Outra distin\u00e7\u00e3o entre esses dois tipos de fun\u00e7\u00f5es \u00e9 o grau. As fun\u00e7\u00f5es lineares s\u00e3o sempre de primeiro grau, mas as fun\u00e7\u00f5es n\u00e3o lineares podem ser de segundo grau, terceiro grau, quarto grau, etc.<\/p>\n

Fun\u00e7\u00f5es lineares e n\u00e3o lineares tamb\u00e9m diferem em continuidade. Porque as fun\u00e7\u00f5es lineares s\u00e3o sempre cont\u00ednuas em todo o seu dom\u00ednio e, por outro lado, as fun\u00e7\u00f5es n\u00e3o lineares podem apresentar algum tipo de descontinuidade.<\/p>\n

Voc\u00ea pode saber mais sobre isso no seguinte link:<\/p>\n

\u27a4<\/span> Veja:<\/strong> O que s\u00e3o fun\u00e7\u00f5es lineares?<\/a><\/span> <\/p>\n

<\/span> Tipos de fun\u00e7\u00f5es n\u00e3o lineares<\/span><\/h2>\n

Depois de vermos a defini\u00e7\u00e3o de uma fun\u00e7\u00e3o n\u00e3o linear, veremos quais s\u00e3o todos os tipos de fun\u00e7\u00f5es n\u00e3o lineares.<\/p>\n

<\/span> fun\u00e7\u00f5es quadr\u00e1ticas<\/span><\/h3>\n

Uma fun\u00e7\u00e3o quadr\u00e1tica<\/strong> \u00e9 uma fun\u00e7\u00e3o polinomial quadr\u00e1tica, ou em outras palavras, \u00e9 uma fun\u00e7\u00e3o cujo maior expoente \u00e9 2.<\/p>\n

Portanto, a f\u00f3rmula para uma fun\u00e7\u00e3o quadr\u00e1tica \u00e9:<\/p>\n<\/p>\n

\"f(x)=ax^2+bx+c\"<\/p>\n<\/p>\n

Ouro<\/p>\n<\/p>\n

\"ax^2\"<\/p>\n

\u00e9 o termo quadr\u00e1tico,<\/p>\n

\"bx\"<\/p>\n

o termo linear e<\/p>\n

\"c\"<\/p>\n

o termo independente da fun\u00e7\u00e3o polinomial.<\/p>\n

Exemplos de fun\u00e7\u00f5es quadr\u00e1ticas ou fun\u00e7\u00f5es polinomiais quadr\u00e1ticas:<\/p>\n<\/p>\n

\"f(x)=3x^2-5x+1\\qquad<\/p>\n<\/p>\n

Representar uma fun\u00e7\u00e3o quadr\u00e1tica num gr\u00e1fico \u00e9 relativamente f\u00e1cil e, al\u00e9m disso, \u00e9 sempre uma par\u00e1bola. No entanto, a forma da par\u00e1bola depende do sinal do coeficiente l\u00edder<\/p>\n<\/p>\n

\"a\"<\/p>\n

da fun\u00e7\u00e3o. Voc\u00ea pode ver como esse tipo de fun\u00e7\u00e3o n\u00e3o linear \u00e9 representado no seguinte link:<\/p>\n

\u27a4<\/span> Veja:<\/strong> Representa\u00e7\u00e3o gr\u00e1fica de fun\u00e7\u00f5es quadr\u00e1ticas<\/a><\/span> <\/p>\n

<\/span> Fun\u00e7\u00f5es de proporcionalidade inversa<\/span><\/h3>\n

Uma fun\u00e7\u00e3o de proporcionalidade inversa<\/strong> \u00e9 aquela fun\u00e7\u00e3o que conecta duas quantidades inversamente proporcionais.<\/p>\n

Nota: duas quantidades s\u00e3o inversamente proporcionais se uma aumenta quando a outra diminui e vice-versa<\/p>\n

Este tipo de fun\u00e7\u00f5es n\u00e3o lineares \u00e9 definido pela seguinte f\u00f3rmula:<\/p>\n<\/p>\n

\"y=\\cfrac{k}{x}\"<\/p>\n<\/p>\n

Ouro<\/p>\n<\/p>\n

\"k\"<\/p>\n

\u00e9 uma constante chamada raz\u00e3o de proporcionalidade.<\/p>\n

Exemplos de fun\u00e7\u00f5es de proporcionalidade inversa:<\/p>\n<\/p>\n

\"y=\\cfrac{5}{x}<\/p>\n<\/p>\n

As fun\u00e7\u00f5es de proporcionalidade inversa s\u00e3o mais dif\u00edceis de representar porque sempre t\u00eam ass\u00edntotas. Voc\u00ea pode ver como isso acontece no seguinte link:<\/p>\n

\u27a4<\/span> Veja:<\/strong> Representa\u00e7\u00e3o de fun\u00e7\u00f5es de proporcionalidade inversa<\/a><\/span><\/p>\n

<\/span> fun\u00e7\u00f5es irracionais<\/span><\/h3>\n

Uma fun\u00e7\u00e3o irracional<\/strong> , tamb\u00e9m chamada de fun\u00e7\u00e3o radical<\/strong> , \u00e9 uma fun\u00e7\u00e3o n\u00e3o linear que possui a vari\u00e1vel independente x sob o s\u00edmbolo de uma raiz.<\/p>\n

Como voc\u00ea j\u00e1 sabe, o resultado de uma raiz pode ser positivo ou negativo. De modo que a representa\u00e7\u00e3o de uma fun\u00e7\u00e3o irracional (ou radical) possui duas curvas poss\u00edveis, embora normalmente apenas o ramo positivo seja representado.<\/p>\n

\u27a4<\/span> Veja:<\/strong> Representa\u00e7\u00e3o gr\u00e1fica de fun\u00e7\u00f5es irracionais<\/a><\/span><\/p>\n

<\/span> fun\u00e7\u00f5es exponenciais<\/span><\/h3>\n

Fun\u00e7\u00f5es exponenciais<\/strong> s\u00e3o fun\u00e7\u00f5es n\u00e3o lineares nas quais a vari\u00e1vel independente x<\/em> aparece no expoente de uma pot\u00eancia. Em outras palavras, uma fun\u00e7\u00e3o exponencial \u00e9:<\/p>\n<\/p>\n

\"f(x)=a^x\"<\/p>\n<\/p>\n

Ouro<\/p>\n<\/p>\n

\"a\"<\/p>\n

\u00e9 um n\u00famero real positivo e diferente de 1.<\/p>\n

Como o nome sugere, o gr\u00e1fico de uma fun\u00e7\u00e3o exponencial cresce exponencialmente, portanto mais pontos da fun\u00e7\u00e3o devem ser calculados para represent\u00e1-la corretamente.<\/p>\n

\u27a4<\/span> Veja:<\/strong> Representa\u00e7\u00e3o gr\u00e1fica de fun\u00e7\u00f5es exponenciais<\/a><\/span><\/p>\n

<\/span> fun\u00e7\u00f5es logar\u00edtmicas<\/span><\/h3>\n

Fun\u00e7\u00f5es logar\u00edtmicas<\/strong> s\u00e3o fun\u00e7\u00f5es cuja vari\u00e1vel independente x<\/em> faz parte do argumento de um logaritmo. Em outras palavras, uma fun\u00e7\u00e3o logar\u00edtmica \u00e9 uma fun\u00e7\u00e3o n\u00e3o linear que tem a seguinte forma:<\/p>\n<\/p>\n

\"f(x)=\\log_a<\/p>\n<\/p>\n

Ouro<\/p>\n<\/p>\n

\"a\"<\/p>\n

\u00e9 necessariamente um n\u00famero real positivo e diferente de 1.<\/p>\n

O inverso da fun\u00e7\u00e3o logar\u00edtmica \u00e9 a fun\u00e7\u00e3o exponencial. Assim, os gr\u00e1ficos de uma fun\u00e7\u00e3o logar\u00edtmica e de uma fun\u00e7\u00e3o exponencial s\u00e3o sim\u00e9tricos em rela\u00e7\u00e3o \u00e0 reta y=x se ambos tiverem a mesma base.<\/p>\n

\u27a4<\/span> Veja:<\/strong> Representa\u00e7\u00e3o gr\u00e1fica de fun\u00e7\u00f5es logar\u00edtmicas<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Neste artigo, voc\u00ea aprender\u00e1 o que s\u00e3o fun\u00e7\u00f5es n\u00e3o lineares. Tamb\u00e9m explicamos as diferen\u00e7as entre fun\u00e7\u00f5es lineares e fun\u00e7\u00f5es n\u00e3o lineares. E, al\u00e9m disso, voc\u00ea poder\u00e1 ver quais s\u00e3o os diferentes tipos de fun\u00e7\u00f5es n\u00e3o lineares com exemplos. O que \u00e9 uma fun\u00e7\u00e3o n\u00e3o linear? Uma fun\u00e7\u00e3o n\u00e3o linear \u00e9 uma fun\u00e7\u00e3o cuja representa\u00e7\u00e3o gr\u00e1fica …<\/p>\n

Fun\u00e7\u00f5es n\u00e3o lineares<\/span> Leia mais »<\/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-371","post","type-post","status-publish","format-standard","hentry","category-representacao-de-funcao"],"yoast_head":"\nFun\u00e7\u00f5es n\u00e3o lineares - Mathority<\/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\/funcoes-nao-lineares\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fun\u00e7\u00f5es n\u00e3o lineares - Mathority\" \/>\n<meta property=\"og:description\" content=\"Neste artigo, voc\u00ea aprender\u00e1 o que s\u00e3o fun\u00e7\u00f5es n\u00e3o lineares. 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Tamb\u00e9m explicamos as diferen\u00e7as entre fun\u00e7\u00f5es lineares e fun\u00e7\u00f5es n\u00e3o lineares. E, al\u00e9m disso, voc\u00ea poder\u00e1 ver quais s\u00e3o os diferentes tipos de fun\u00e7\u00f5es n\u00e3o lineares com exemplos. O que \u00e9 uma fun\u00e7\u00e3o n\u00e3o linear? Uma fun\u00e7\u00e3o n\u00e3o linear \u00e9 uma fun\u00e7\u00e3o cuja representa\u00e7\u00e3o gr\u00e1fica … Fun\u00e7\u00f5es n\u00e3o lineares Leia mais »","og_url":"https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/","article_published_time":"2023-07-04T08:20:07+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-fonction-quadratique.webp"}],"author":"Equipe Mathoridade","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Equipe Mathoridade","Est. tempo de leitura":"4 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/"},"author":{"name":"Equipe Mathoridade","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00"},"headline":"Fun\u00e7\u00f5es n\u00e3o lineares","datePublished":"2023-07-04T08:20:07+00:00","dateModified":"2023-07-04T08:20:07+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/"},"wordCount":837,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"articleSection":["Representa\u00e7\u00e3o de fun\u00e7\u00e3o"],"inLanguage":"pt-BR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/","url":"https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/","name":"Fun\u00e7\u00f5es n\u00e3o lineares - Mathority","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/#website"},"datePublished":"2023-07-04T08:20:07+00:00","dateModified":"2023-07-04T08:20:07+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/pt\/funcoes-nao-lineares\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/pt\/"},{"@type":"ListItem","position":2,"name":"Fun\u00e7\u00f5es n\u00e3o lineares"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/pt\/#website","url":"https:\/\/mathority.org\/pt\/","name":"Mathority","description":"Onde a curiosidade encontra o c\u00e1lculo!","publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/pt\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"pt-BR"},{"@type":"Organization","@id":"https:\/\/mathority.org\/pt\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/pt\/","logo":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00","name":"Equipe Mathoridade","image":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Equipe Mathoridade"},"sameAs":["http:\/\/mathority.org\/pt"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/371","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/comments?post=371"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/371\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/media?parent=371"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/categories?post=371"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/tags?post=371"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}