{"id":128268,"date":"2017-11-06T10:35:47","date_gmt":"2017-11-06T12:35:47","guid":{"rendered":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/?p=128268"},"modified":"2026-05-19T18:52:49","modified_gmt":"2026-05-19T20:52:49","slug":"funcao-afim","status":"publish","type":"post","link":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/funcao-afim","title":{"rendered":"Fun\u00e7\u00e3o Afim"},"content":{"rendered":"<p>A\u00a0<b>fun\u00e7\u00e3o afim, ou fun\u00e7\u00e3o do 1\u00ba grau<\/b>, \u00e9 definida pela f\u00f3rmula f (x) = ax + b\\), onde a (coeficiente angular) e b (coeficiente linear) s\u00e3o n\u00fameros reais, com a #\u00a0 0\\). Seu gr\u00e1fico \u00e9 sempre uma reta n\u00e3o vertical, que corta o eixo y\\ no ponto (0, b) e \u00e9 crescente se a &gt; 0 ou decrescente se a &lt;0.<\/p>\n<p>Uma<b>\u00a0fun\u00e7\u00e3o linear<\/b>\u00a0\u00e9 uma fun\u00e7\u00e3o que representa uma reta no plano cartesiano.<\/p>\n<p>Por exemplo, y = 3x &#8211; 2 representa uma reta no plano cartesiano e, portanto, representa uma fun\u00e7\u00e3o linear. Como y pode ser substitu\u00eddo por f(x), essa fun\u00e7\u00e3o pode ser escrita como f(x) = 3x &#8211; 2.<\/p>\n<p><span class=\"HwtZe\" lang=\"pt\"><span class=\"jCAhz ChMk0b\"><span class=\"ryNqvb\">Uma\u00a0<b>fun\u00e7\u00e3o linear<\/b>\u00a0tem a forma f(x) = mx + b, onde &#8216;m&#8217; e &#8216;b&#8217; s\u00e3o n\u00fameros reais.<\/span><\/span>\u00a0<span class=\"jCAhz ChMk0b\"><span class=\"ryNqvb\">N\u00e3o parece a forma reduzida da equa\u00e7\u00e3o da reta, expressa como y = mx + b. Sim, isso ocorre porque uma fun\u00e7\u00e3o linear representa uma reta, ou seja, seu gr\u00e1fico \u00e9 uma reta.<\/span><\/span><\/span><\/p>\n<p><span class=\"HwtZe\" lang=\"pt\"><span class=\"jCAhz ChMk0b\"><span class=\"ryNqvb\"><b>Aqui,<\/b><\/span><\/span><\/span><\/p>\n<p><span class=\"HwtZe\" lang=\"pt\"><span class=\"jCAhz ChMk0b\"><span class=\"ryNqvb\">&#8216;m&#8217; \u00e9 o coeficiente angular da reta<br \/>\n&#8216;b&#8217; \u00e9 o coeficiente linear da reta<br \/>\n&#8216;x&#8217; \u00e9 a vari\u00e1vel independente<br \/>\n&#8216;y&#8217; (ou f(x)) \u00e9 a vari\u00e1vel dependente.<\/span><\/span><\/span><\/p>\n<p><span class=\"ryNqvb\"><span lang=\"pt\">Uma fun\u00e7\u00e3o linear \u00e9 uma fun\u00e7\u00e3o alg\u00e9brica. Isso ocorre porque ela envolve apenas opera\u00e7\u00f5es alg\u00e9bricas.<\/span><\/span><\/p>\n<p>A\u00a0<strong>fun\u00e7\u00e3o afim<\/strong>\u00a0\u00e9 tamb\u00e9m conhecida como fun\u00e7\u00e3o polinomial de grau 1 ou ent\u00e3o, fun\u00e7\u00e3o\u00a0linear.<\/p>\n<p>A generaliza\u00e7\u00e3o da fun\u00e7\u00e3o afim \u00e9 f(x) = a x + b .<\/p>\n<p><strong>Exemplo:<\/strong>\u00a0y(x) = 3x \u2013 4<\/p>\n<p>Nessa fun\u00e7\u00e3o, a = 3 e b = &#8211; 4<\/p>\n<p class=\"imagem\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-128269\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-1.png\" alt=\"funcao-afim-1\" width=\"400\" height=\"288\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-1.png 400w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-1-300x216.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p><strong>Exemplo:<\/strong> y(x) = x<\/p>\n<p>Nessa fun\u00e7\u00e3o, a = 1 e b = 0<\/p>\n<p class=\"imagem\"><img decoding=\"async\" class=\"alignnone size-full wp-image-128270\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-2.png\" alt=\"funcao-afim-2\" width=\"399\" height=\"287\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-2.png 399w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-2-300x216.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<p>Na fun\u00e7\u00e3o afim, o coeficiente <strong>a<\/strong> \u00e9 denominado <strong>coeficiente angular<\/strong>, que est\u00e1 associado ao\u00a0crescimento ou decrescimento.<\/p>\n<p>Coeficiente angular a demonstrando crescimento (<span style=\"color: #ff0000;\"> a &gt; 0<\/span> )<\/p>\n<p><strong>Exemplo:<\/strong> f(x) = <span style=\"color: #ff0000;\">80<\/span>x<\/p>\n<p class=\"imagem\"><img decoding=\"async\" class=\"alignnone size-full wp-image-128271\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-3.png\" alt=\"funcao-afim-3\" width=\"440\" height=\"314\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-3.png 440w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-3-300x214.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p>Coeficiente angular a demonstrando decrescimento (<span style=\"color: #ff0000;\"> a &lt; 0<\/span> )<\/p>\n<p><strong>Exemplo:<\/strong> f(x) = <span style=\"color: #ff0000;\">&#8211; 45<\/span>x<\/p>\n<p class=\"imagem\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128272\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-4.png\" alt=\"funcao-afim-4\" width=\"470\" height=\"331\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-4.png 470w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-4-300x211.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p>Na fun\u00e7\u00e3o afim, o coeficiente <strong>b<\/strong> \u00e9 denominado <strong>coeficiente linear<\/strong>, que est\u00e1 associado ao\u00a0deslocamento da fun\u00e7\u00e3o.<\/p>\n<p><strong>Exemplo:<\/strong> <em>f<\/em><sub>1<\/sub>(x) = 3x + 4 <strong>e<\/strong> <em>f<\/em><sub>2<\/sub>(x) = 3x \u2212 4<\/p>\n<p><strong>Aten\u00e7\u00e3o:<\/strong> quando fazemos um deslocamento da fun\u00e7\u00e3o para a direita , estamos subtraindo\u00a0uma constante. Basta notar que <em>f<\/em>2(x) = <em>f<\/em>1(x \u2212 8).<\/p>\n<p>Para deslocar a fun\u00e7\u00e3o para a esquerda , precisamos somar uma constante.<\/p>\n<p class=\"imagem\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128273\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-5.png\" alt=\"funcao-afim-5\" width=\"439\" height=\"327\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-5.png 439w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-afim-5-300x223.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><\/p>\n<p><strong>Fonte:<\/strong>\u00a0Col\u00e9gio S\u00e3o Francisco\/Luisa Boccardo Burini<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A\u00a0fun\u00e7\u00e3o afim, ou fun\u00e7\u00e3o do 1\u00ba grau, \u00e9 definida pela f\u00f3rmula f (x) = ax + b\\), onde a (coeficiente angular) e b (coeficiente linear) s\u00e3o n\u00fameros reais, com a #\u00a0 0\\). Seu gr\u00e1fico \u00e9 sempre uma reta n\u00e3o vertical, que corta o eixo y\\ no ponto (0, b) e \u00e9 crescente se a &gt; [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[414],"tags":[],"class_list":["post-128268","post","type-post","status-publish","format-standard","hentry","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Fun\u00e7\u00e3o Afim, Coeficiente Angular, Matem\u00e1tica Fun\u00e7\u00e3o Afim<\/title>\n<meta name=\"description\" content=\"Fun\u00e7\u00e3o Afim, Coeficiente Angular, Matem\u00e1tica, Reta, Linear, N\u00fameros, Equa\u00e7\u00e3o, Gr\u00e1fico, Crescimento, Exemplo, Fun\u00e7\u00e3o Afim\" \/>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, 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