{"id":14771,"date":"2018-04-22T16:10:55","date_gmt":"2018-04-22T15:10:55","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14771"},"modified":"2022-01-09T23:56:11","modified_gmt":"2022-01-09T23:56:11","slug":"partes-dos-graficos-de-duas-funcoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14771","title":{"rendered":"Partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_14771' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14771' class='GTTabs_curr'><a  id=\"14771_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14771' ><a  id=\"14771_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_14771'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-11.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14773\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14773\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-11.png\" data-orig-size=\"430,537\" 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\/9V2Pag117-11.png\" class=\"alignright wp-image-14773\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-11-240x300.png\" alt=\"\" width=\"300\" height=\"375\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-11-240x300.png 240w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-11.png 430w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/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>o ponto <em>O<\/em> \u00e9 a origem do referencial;<\/li>\n<li>o gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em> \u00e9 uma reta que passa na origem do referencial;<\/li>\n<li>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 definida por \\(f\\left( x \\right) = &#8211; 2{x^2}\\);<\/li>\n<li>o ponto <em>P<\/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 abcissa igual a 2.<\/li>\n<\/ul>\n<ol>\n<li>Qual das express\u00f5es seguintes \u00e9 equivalente a\u00a0\\(g\\left( x \\right)\\)?<br \/>\n[A] \\( &#8211; 2x\\)\u00a0 \u00a0 \u00a0 [B] \\( &#8211; 4x\\)\u00a0 \u00a0 \u00a0 [C] \\( &#8211; 2x &#8211; 4\\)\u00a0 \u00a0 \u00a0 [D]\u00a0\\( &#8211; 4x &#8211; 2\\)<\/li>\n<li>Resolve a equa\u00e7\u00e3o seguinte.\\[ &#8211; 2{x^2} = 4 &#8211; 3\\left( {x + 1} \\right)\\]Apresenta todo os c\u00e1lculos que efetuares.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14771' onClick='GTTabs_show(1,14771)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14771'>\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\/9V2Pag117-11.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14773\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14773\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-11.png\" data-orig-size=\"430,537\" 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\/9V2Pag117-11.png\" class=\"alignright wp-image-14773\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-11-240x300.png\" alt=\"\" width=\"300\" height=\"375\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-11-240x300.png 240w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-11.png 430w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/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>\n<p>o ponto <em>O<\/em> \u00e9 a origem do referencial;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>o gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em> \u00e9 uma reta que passa na origem do referencial;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 definida por \\(f\\left( x \\right) = &#8211; 2{x^2}\\);<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>o ponto <em>P<\/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 abcissa igual a 2.<\/p>\n<\/blockquote>\n<\/li>\n<\/ul>\n<p>\u00ad<\/p>\n<ol>\n<li>Comecemos por determinar a ordenada do ponto <em>P<\/em>:\\[{y_P} = f\\left( 2 \\right) = &#8211; 2 \\times {2^2} = &#8211; 8\\]Como o declive da reta <em>OP<\/em> \u00e9\u00a0\\({m_{OP}} = \\frac{{ &#8211; 8 &#8211; 0}}{{2 &#8211; 0}} = &#8211; 4\\) e a ordenada na origem \u00e9 zero, ent\u00e3o a fun\u00e7\u00e3o <em>g<\/em> pode ser definida por\u00a0\\(g\\left( x \\right) = &#8211; 4x\\).<br \/>\nPortanto, a alternativa correta \u00e9 a [<strong>B<\/strong>].<br \/>\n\u00ad<\/li>\n<li>Resolvendo a equa\u00e7\u00e3o, temos:<br \/>\n\\[\\begin{array}{*{20}{l}}{ &#8211; 2{x^2} = 4 &#8211; 3\\left( {x + 1} \\right)}&amp; \\Leftrightarrow &amp;{ &#8211; 2{x^2} + 3x &#8211; 1 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{ &#8211; 3 \\mp \\sqrt {9 &#8211; 8} }}{{ &#8211; 4}}}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{ &#8211; 3 \\mp 1}}{{ &#8211; 4}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{1}{2}}&amp; \\vee &amp;{x = 1}\\end{array}}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14771' onClick='GTTabs_show(0,14771)'>&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: o ponto O \u00e9 a origem do referencial; o gr\u00e1fico da fun\u00e7\u00e3o g&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14774,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,249],"tags":[426,345,499,500],"series":[],"class_list":["post-14771","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-afim","tag-funcao-quadratica","tag-parabola"],"views":2118,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag117-11a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14771","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=14771"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14771\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14774"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14771"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14771"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14771"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}