{"id":14778,"date":"2018-04-22T16:53:49","date_gmt":"2018-04-22T15:53:49","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14778"},"modified":"2022-01-09T23:58:38","modified_gmt":"2022-01-09T23:58:38","slug":"partes-dos-graficos-de-duas-funcoes-novamente","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14778","title":{"rendered":"Partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, novamente"},"content":{"rendered":"<p><ul id='GTTabs_ul_14778' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14778' class='GTTabs_curr'><a  id=\"14778_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14778' ><a  id=\"14778_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_14778'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14779\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14779\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12.png\" data-orig-size=\"629,532\" 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\u00e1ficos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12.png\" class=\"alignright wp-image-14779\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12-300x254.png\" alt=\"\" width=\"400\" height=\"338\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12-300x254.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12.png 629w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>Na figura, est\u00e3o representadas, num referencial cartesiano, partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, <em>f<\/em> e <em>g<\/em>.<br \/>\nSabe-se que:<\/p>\n<ul>\n<li>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 uma fun\u00e7\u00e3o quadr\u00e1tica definida por \\(f\\left( x \\right) = a{x^2}\\), sendo <em>a<\/em> um n\u00famero positivo;<\/li>\n<li>a fun\u00e7\u00e3o <em>g<\/em> \u00e9 uma fun\u00e7\u00e3o de proporcionalidade inversa;<\/li>\n<li>o ponto <em>B<\/em> pertence ao gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em> e ao gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em> e tem coordenadas \\(\\left( {2,\\;6} \\right)\\);<\/li>\n<li>o ponto <em>C<\/em> pertence ao gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em> e tem coordenadas \\(\\left( {c;\\;1,2} \\right)\\), sendo <em>c<\/em> um n\u00famero positivo.<\/li>\n<\/ul>\n<ol>\n<li>Qual e o valor de \\(f\\left( { &#8211; 2} \\right)\\)?<br \/>\n[<strong>A<\/strong>] \\( &#8211; 6\\)\u00a0 \u00a0 \u00a0 [<strong>B<\/strong>] \\(6\\)\u00a0 \u00a0 \u00a0 [<strong>C<\/strong>] \\( &#8211; 4\\)\u00a0 \u00a0 \u00a0 [<strong>D<\/strong>]\u00a0\\(4\\)<\/li>\n<li>Qual \u00e9 o valor de <em>c<\/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_14778' onClick='GTTabs_show(1,14778)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14778'>\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\/9V2Pag117-12.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14779\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14779\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12.png\" data-orig-size=\"629,532\" 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\u00e1ficos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12.png\" class=\"alignright wp-image-14779\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12-300x254.png\" alt=\"\" width=\"400\" height=\"338\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12-300x254.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12.png 629w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>Na figura, est\u00e3o representadas, num referencial cartesiano, 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><p>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 uma fun\u00e7\u00e3o quadr\u00e1tica definida por \\(f\\left( x \\right) = a{x^2}\\), sendo <em>a<\/em> um n\u00famero positivo;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>a fun\u00e7\u00e3o <em>g<\/em> \u00e9 uma fun\u00e7\u00e3o de proporcionalidade inversa;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>o ponto <em>B<\/em> pertence ao gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em> e ao gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em> e tem coordenadas \\(\\left( {2,\\;6} \\right)\\);<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>o ponto <em>C<\/em> pertence ao gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em> e tem coordenadas \\(\\left( {c;\\;1,2} \\right)\\), sendo <em>c<\/em> um n\u00famero positivo.<\/p><\/blockquote>\n<\/li>\n<\/ul>\n<p>\u00ad<\/p>\n<ol>\n<li>Ora, \\(f\\left( { &#8211; 2} \\right) = a \\times {\\left( { &#8211; 2} \\right)^2} = a \\times {\\left( { + 2} \\right)^2} = f\\left( 2 \\right) = 6\\).<br \/>\nLogo, a alternativa correta \u00e9 a [<strong>B<\/strong>].<br \/>\n\u00ad<\/li>\n<li>Como a fun\u00e7\u00e3o <em>g<\/em> \u00e9 uma fun\u00e7\u00e3o de proporcionalidade inversa, ser\u00e1 do tipo\u00a0\\(x \\times y = k\\), com <em>k<\/em> constante e real. Como o ponto <em>B<\/em> \u00e9 um ponto do gr\u00e1fico de <em>g<\/em>, ent\u00e3o\u00a0\\(\\begin{array}{*{20}{c}}{2 \\times 6 = k}&amp; \\Leftrightarrow &amp;{k = 12}\\end{array}\\). Logo, a fun\u00e7\u00e3o <em>g<\/em> pode ser definida por\u00a0\\(g\\left( x \\right) = \\frac{{12}}{x}\\).<br \/>\nFinalmente, como <em>C<\/em> \u00e9 um ponto do gr\u00e1fico de <em>g<\/em>, temos:\\[\\begin{array}{*{20}{l}}{g\\left( c \\right) = 1,2}&amp; \\Leftrightarrow &amp;{\\frac{{12}}{c} = 1,2}\\\\{}&amp; \\Leftrightarrow &amp;{c = 10}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14778' onClick='GTTabs_show(0,14778)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, est\u00e3o representadas, num referencial cartesiano, partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, f e g. Sabe-se que: a fun\u00e7\u00e3o f \u00e9 uma fun\u00e7\u00e3o quadr\u00e1tica definida por \\(f\\left( x \\right) =&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14781,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,249],"tags":[426,503,499],"series":[],"class_list":["post-14778","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-proporcionalidade-inversa-e-funcoes-algebricas","tag-9-o-ano","tag-funcao-de-proporcionalidade-inversa","tag-funcao-quadratica"],"views":1922,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-12a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14778","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=14778"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14778\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14781"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14778"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14778"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14778"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14778"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}