{"id":14689,"date":"2018-04-19T18:11:14","date_gmt":"2018-04-19T17:11:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14689"},"modified":"2022-01-09T22:50:30","modified_gmt":"2022-01-09T22:50:30","slug":"uma-representacao-grafica-de-quatro-funcoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14689","title":{"rendered":"Uma representa\u00e7\u00e3o gr\u00e1fica de quatro fun\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_14689' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14689' class='GTTabs_curr'><a  id=\"14689_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14689' ><a  id=\"14689_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_14689'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14690\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14690\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-3.png\" data-orig-size=\"591,476\" 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\/9V2Pag112-3.png\" class=\"alignright wp-image-14690\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-3-300x242.png\" alt=\"\" width=\"400\" height=\"322\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-3-300x242.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-3.png 591w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>Num referencial est\u00e3o representas as fun\u00e7\u00f5es <em>f<\/em>, <em>g<\/em>, <em>h<\/em> e <em>j<\/em>, que s\u00e3o, respetivamente, uma fun\u00e7\u00e3o quadr\u00e1tica, uma fun\u00e7\u00e3o afim, uma fun\u00e7\u00e3o de proporcionalidade direta e uma fun\u00e7\u00e3o constante.<\/p>\n<ol>\n<li>Define as fun\u00e7\u00f5es <em>f<\/em>, <em>g<\/em>, <em>h<\/em> e <em>j<\/em>\u00a0recorrendo a express\u00f5es alg\u00e9bricas.<\/li>\n<li>Determina os valores de x tais que:<\/li>\n<\/ol>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\\(g\\left( x \\right) = j\\left( x \\right)\\)<\/li>\n<li>\\(f\\left( x \\right) = h\\left( x \\right)\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14689' onClick='GTTabs_show(1,14689)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14689'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Os gr\u00e1ficos das fun\u00e7\u00f5es do tipo\u00a0\\(f\\left( x \\right) = a{x^2}\\), com\u00a0\\(a \\ne 0\\), s\u00e3o <strong>par\u00e1bolas de eixo vertical e v\u00e9rtice na origem<\/strong>.<\/p>\n<\/blockquote>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14690\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14690\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-3.png\" data-orig-size=\"591,476\" 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\/9V2Pag112-3.png\" class=\"alignright wp-image-14690\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-3-300x242.png\" alt=\"\" width=\"400\" height=\"322\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-3-300x242.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-3.png 591w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>As fun\u00e7\u00f5es <em>f<\/em>, <em>g<\/em>, <em>h<\/em> e <em>j<\/em>\u00a0podem ser definidas pelas seguintes express\u00f5es alg\u00e9bricas:<br \/>\n&#8211; \\(f\\left( x \\right) = 3{x^2}\\)<br \/>\n&#8211;\u00a0\\(g\\left( x \\right) = &#8211; 2x + 2\\)<br \/>\n&#8211;\u00a0\\(h\\left( x \\right) = 3x\\)<br \/>\n&#8211;\u00a0\\(j\\left( x \\right) = 4\\)<\/p>\n<p><strong>Explica\u00e7\u00e3o<\/strong>:<br \/>\nComo a fun\u00e7\u00e3o <em>f<\/em> \u00e9 definida por uma express\u00e3o do tipo \\(f\\left( x \\right) = a{x^2}\\) e \\(f\\left( 1 \\right) = 3\\), vem:<br \/>\n\\[\\begin{array}{*{20}{l}}{f\\left( 1 \\right) = 3}&amp; \\Leftrightarrow &amp;{a \\times {1^2} = 3}\\\\{}&amp; \\Leftrightarrow &amp;{a = 3}\\end{array}\\]<br \/>\nA reta azul tem declive\u00a0\\(m = \\frac{{2 &#8211; 0}}{{0 &#8211; 1}} = &#8211; 2\\) e a ordenada na origem \u00e9 2, pois o ponto de coordenadas \\(\\left( {0,\\;2} \\right)\\) \u00e9 um dos seus pontos.<br \/>\nA reta verde tem declive \\(m = \\frac{{3 &#8211; 0}}{{1 &#8211; 0}} = 3\\) e a ordenada na origem \u00e9 nula.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>Determina os valores de x tais que:<\/li>\n<\/ol>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\\(g\\left( x \\right) = j\\left( x \\right)\\)<br \/>\n\\[\\begin{array}{*{20}{l}}{g\\left( x \\right) = j\\left( x \\right)}&amp; \\Leftrightarrow &amp;{ &#8211; 2x + 2 = 4}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; 2x = 2}\\\\{}&amp; \\Leftrightarrow &amp;{x = &#8211; 1}\\end{array}\\]<\/li>\n<li>\\(f\\left( x \\right) = h\\left( x \\right)\\)<br \/>\n\\[\\begin{array}{*{20}{l}}{f\\left( x \\right) = h\\left( x \\right)}&amp; \\Leftrightarrow &amp;{3{x^2} = 3x}\\\\{}&amp; \\Leftrightarrow &amp;{3{x^2} &#8211; 3x = 0}\\\\{}&amp; \\Leftrightarrow &amp;{3x\\left( {x &#8211; 1} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{3x = 0}&amp; \\vee &amp;{x &#8211; 1 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&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_14689' onClick='GTTabs_show(0,14689)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Num referencial est\u00e3o representas as fun\u00e7\u00f5es f, g, h e j, que s\u00e3o, respetivamente, uma fun\u00e7\u00e3o quadr\u00e1tica, uma fun\u00e7\u00e3o afim, uma fun\u00e7\u00e3o de proporcionalidade direta e uma fun\u00e7\u00e3o constante. Define as&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14692,"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],"series":[],"class_list":["post-14689","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"],"views":2525,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-3a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14689","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=14689"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14689\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14692"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14689"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}