{"id":14654,"date":"2018-04-18T11:36:23","date_gmt":"2018-04-18T10:36:23","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14654"},"modified":"2022-01-09T22:26:29","modified_gmt":"2022-01-09T22:26:29","slug":"graficos-de-duas-funcoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14654","title":{"rendered":"Gr\u00e1ficos de duas fun\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_14654' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14654' class='GTTabs_curr'><a  id=\"14654_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14654' ><a  id=\"14654_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_14654'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14657\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14657\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8.png\" data-orig-size=\"478,412\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Gr\u00e1fico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8.png\" class=\"alignright wp-image-14657\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8-300x259.png\" alt=\"\" width=\"320\" height=\"276\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8-300x259.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8.png 478w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a>Na figura, est\u00e3o representados, num referencial cartesiano, os pontos <em>A<\/em> e <em>B<\/em> e partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, <em>f<\/em> e <em>g<\/em>.<\/p>\n<p>Sabe-se que:<\/p>\n<ul>\n<li>o ponto <em>O<\/em> \u00e9 a origem do referencial;<\/li>\n<li>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 uma fun\u00e7\u00e3o de proporcionalidade direta;<\/li>\n<li>a fun\u00e7\u00e3o <em>g<\/em> \u00e9 uma fun\u00e7\u00e3o de proporcionalidade inversa;<\/li>\n<li>o ponto <em>A<\/em> pertence ao gr\u00e1fico de <em>f<\/em> e tem coordenadas \\(\\left( {8,\\;6} \\right)\\);<\/li>\n<li>o ponto <em>B<\/em> pertence ao gr\u00e1fico de <em>f<\/em> e ao gr\u00e1fico de <em>g<\/em> e tem abcissa igual a 4.<\/li>\n<\/ul>\n<ol>\n<li>Qual das seguintes express\u00f5es \u00e9 equivalente a\u00a0\\(g\\left( x \\right)\\)?<br \/>\n[A] \\(\\frac{6}{x}\\) \u00a0 \u00a0\u00a0 [B] \\(\\frac{8}{x}\\) \u00a0 \u00a0\u00a0 [C] \\(\\frac{{10}}{x}\\) \u00a0 \u00a0\u00a0 [D]\u00a0\\(\\frac{{12}}{x}\\)<\/li>\n<li>Designemos por <em>C<\/em> a imagem do ponto <em>A<\/em> por meio de uma reflex\u00e3o de eixo <em>Ox<\/em> (o ponto <em>C<\/em> n\u00e3o est\u00e1 representado na figura).<br \/>\nDetermina o per\u00edmetro do tri\u00e2ngulo [<em>AOC<\/em>].<br \/>\nMostra como chegaste \u00e0 tua resposta.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14654' onClick='GTTabs_show(1,14654)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14654'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14657\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14657\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8.png\" data-orig-size=\"478,412\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Gr\u00e1fico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8.png\" class=\"alignright wp-image-14657\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8-300x259.png\" alt=\"\" width=\"320\" height=\"276\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8-300x259.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8.png 478w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a>Na figura, est\u00e3o representados, num referencial cartesiano, os pontos <em>A<\/em> e <em>B<\/em> e partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, <em>f<\/em> e <em>g<\/em>.<br \/>\nSabe-se que:<\/p>\n<\/blockquote>\n<ul>\n<li>\n<blockquote>\n<p>o ponto <em>O<\/em> \u00e9 a origem do referencial;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 uma fun\u00e7\u00e3o de proporcionalidade direta;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>a fun\u00e7\u00e3o <em>g<\/em> \u00e9 uma fun\u00e7\u00e3o de proporcionalidade inversa;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>o ponto <em>A<\/em> pertence ao gr\u00e1fico de <em>f<\/em> e tem coordenadas \\(\\left( {8,\\;6} \\right)\\);<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>o ponto <em>B<\/em> pertence ao gr\u00e1fico de <em>f<\/em> e ao gr\u00e1fico de <em>g<\/em> e tem abcissa igual a 4.<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<\/li>\n<\/ul>\n<ol>\n<li>Como o declive da reta AB \u00e9\u00a0\\({m_{AB}} = \\frac{{6 &#8211; 0}}{{8 &#8211; 0}} = \\frac{3}{4}\\), ent\u00e3o\u00a0\\(f\\left( x \\right) = \\frac{3}{4}x\\).<br \/>\nAssim, a ordenada do ponto B \u00e9\u00a0\\({y_B} = f\\left( 4 \\right) = \\frac{3}{4} \\times 4 = 3\\).<br \/>\nFinalmente, como g \u00e9 uma fun\u00e7\u00e3o de proporcionalidade inversa, temos:\\[\\begin{array}{*{20}{l}}{g\\left( x \\right) = \\frac{{{x_B} \\times {y_B}}}{x}}&amp; \\Leftrightarrow &amp;{g\\left( x \\right) = \\frac{{4 \\times 3}}{x}}\\\\{}&amp; \\Leftrightarrow &amp;{g\\left( x \\right) = \\frac{{12}}{x}}\\end{array}\\]Portanto, a alternativa correta \u00e9 a [D].<br \/>\n\u00ad<\/li>\n<li>Por aplica\u00e7\u00e3o do Teorema de Pit\u00e1goras, vem:\u00a0\\(\\overline {OA} = \\sqrt {{8^2} + {6^2}} = \\sqrt {100} = 10\\).<br \/>\nAssim, o per\u00edmetro do tri\u00e2ngulo [<em>AOC<\/em>] \u00e9\u00a0\\({P_{\\left[ {AOC} \\right]}} = \\overline {AO} + \\overline {OC} + \\overline {AC} = 10 + 10 + 12 = 32\\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14654' onClick='GTTabs_show(0,14654)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, est\u00e3o representados, num referencial cartesiano, os pontos A e B e partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, f e g. Sabe-se que: o ponto O \u00e9 a origem do&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14660,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,249],"tags":[250],"series":[],"class_list":["post-14654","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-proporcionalidade-inversa-e-funcoes-algebricas","tag-proporcionalidade-inversa-2"],"views":3023,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-8a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14654","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14654"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14654\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14660"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14654"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14654"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14654"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14654"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}