{"id":14872,"date":"2018-04-25T12:13:52","date_gmt":"2018-04-25T11:13:52","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14872"},"modified":"2018-04-27T18:55:09","modified_gmt":"2018-04-27T17:55:09","slug":"partes-dos-graficos-de-duas-funcoes-e-um-retangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14872","title":{"rendered":"Partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es e um ret\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_14872' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14872' class='GTTabs_curr'><a  id=\"14872_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14872' ><a  id=\"14872_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_14872'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14873\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14873\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6.png\" data-orig-size=\"505,510\" 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\/9V2Pag125-6.png\" class=\"alignright wp-image-14873\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6-297x300.png\" alt=\"\" width=\"340\" height=\"343\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6-297x300.png 297w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6-150x150.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6-160x160.png 160w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6.png 505w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>No referencial cartesiano da figura, est\u00e3o representadas partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, <em>f<\/em> e <em>g<\/em>, e um trap\u00e9zio.<br \/>\n Sabe-se que:<\/p>\n<ul>\n<li>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 definida por\u00a0\\(f\\left( x \\right) = x\\);<\/li>\n<li>a fun\u00e7\u00e3o <em>g<\/em> \u00e9 definida por\u00a0\\(g\\left( x \\right) = 3{x^2}\\);<\/li>\n<li>o quadril\u00e1tero [<em>ABCD<\/em>] \u00e9 um ret\u00e2ngulo;<\/li>\n<li>os pontos <em>A<\/em> e <em>B<\/em> pertencem ao eixo das abcissas;<\/li>\n<li>o ponto <em>D<\/em> pertence ao gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em>;<\/li>\n<li>os pontos <em>E<\/em> e <em>C<\/em> pertencem ao gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em>;<\/li>\n<li>os pontos <em>A<\/em> e <em>E<\/em> t\u00eam abcissa igual a 1.<\/li>\n<\/ul>\n<ol>\n<li>Determina a medida da \u00e1rea do trap\u00e9zio [ABCE].<br \/>\n Mostra como chegaste \u00e0 tua resposta.<br \/>\n \u00a0<\/li>\n<li>Qual das express\u00f5es seguintes define a fun\u00e7\u00e3o cujo gr\u00e1fico \u00e9 sim\u00e9trico do gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em> relativamente ao eixo das abcissas?<br \/>\n [A] \\(\\frac{1}{3}{x^2}\\)\u00a0 \u00a0 \u00a0 [B] \\( &#8211; \\frac{1}{3}{x^2}\\)\u00a0 \u00a0 \u00a0 [C] \\(3{x^2}\\)\u00a0 \u00a0 \u00a0 [D]\u00a0\\( &#8211; 3{x^2}\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14872' onClick='GTTabs_show(1,14872)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14872'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14873\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14873\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6.png\" data-orig-size=\"505,510\" 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\/9V2Pag125-6.png\" class=\"alignright wp-image-14873\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6-297x300.png\" alt=\"\" width=\"340\" height=\"343\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6-297x300.png 297w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6-150x150.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6-160x160.png 160w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6.png 505w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>No referencial cartesiano da figura, est\u00e3o representadas partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, <em>f<\/em> e <em>g<\/em>, e um trap\u00e9zio.<br \/>\n Sabe-se que:<\/p>\n<ul>\n<li>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 definida por\u00a0\\(f\\left( x \\right) = x\\);<\/li>\n<li>a fun\u00e7\u00e3o <em>g<\/em> \u00e9 definida por\u00a0\\(g\\left( x \\right) = 3{x^2}\\);<\/li>\n<li>o quadril\u00e1tero [<em>ABCD<\/em>] \u00e9 um ret\u00e2ngulo;<\/li>\n<li>os pontos <em>A<\/em> e <em>B<\/em> pertencem ao eixo das abcissas;<\/li>\n<li>o ponto <em>D<\/em> pertence ao gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em>;<\/li>\n<li>os pontos <em>E<\/em> e <em>C<\/em> pertencem ao gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em>;<\/li>\n<li>os pontos <em>A<\/em> e <em>E<\/em> t\u00eam abcissa igual a 1.<\/li>\n<\/ul>\n<ol>\n<li>A ordenada do ponto <em>E<\/em> \u00e9\u00a0\\({y_E} = f\\left( 1 \\right) = 1\\).<br \/>\n As ordenadas dos pontos <em>C<\/em> e\u00a0 <em>D<\/em> s\u00e3o iguais, sendo \\({y_C} = {y_D} = g\\left( 1 \\right) = 3 \\times {1^2} = 3\\).<br \/>\n Determinando a abcissa de <em>C<\/em>, vem:\\[\\begin{array}{*{20}{l}}{f\\left( {{x_C}} \\right) = {y_C}}&amp; \\Leftrightarrow &amp;{{x_C} = {y_c}}\\\\{}&amp; \\Leftrightarrow &amp;{{x_C} = 3}\\end{array}\\]Logo, a medida da \u00e1rea do trap\u00e9zio [ABCE] \u00e9\u00a0\\[\\begin{array}{*{20}{l}}{{A_{\\left[ {ABCE} \\right]}}}&amp; = &amp;{\\frac{{\\overline {BC} + \\overline {AE} }}{2} \\times \\overline {AB} }\\\\{}&amp; = &amp;{\\frac{{3 + 1}}{2} \\times 2}\\\\{}&amp; = &amp;4\\end{array}\\]<\/li>\n<li>A express\u00e3o que define a fun\u00e7\u00e3o cujo gr\u00e1fico \u00e9 sim\u00e9trico do gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em> relativamente ao eixo das abcissas \u00e9 \\( &#8211; g\\left( x \\right) = &#8211; 3{x^2}\\).<br \/>\n Assim, a alternativa correta \u00e9 a [<strong>D<\/strong>].<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14872' onClick='GTTabs_show(0,14872)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado No referencial cartesiano da figura, est\u00e3o representadas partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, f e g, e um trap\u00e9zio. Sabe-se que: a fun\u00e7\u00e3o f \u00e9 definida por\u00a0\\(f\\left( x \\right) = x\\);&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14875,"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-14872","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":4568,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-6a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14872","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=14872"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14872\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14875"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14872"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14872"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14872"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14872"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}