{"id":11798,"date":"2014-02-20T22:07:18","date_gmt":"2014-02-20T22:07:18","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11798"},"modified":"2022-01-22T02:18:45","modified_gmt":"2022-01-22T02:18:45","slug":"defina-a-funcao-por-ramos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11798","title":{"rendered":"Defina a fun\u00e7\u00e3o por ramos"},"content":{"rendered":"<p><ul id='GTTabs_ul_11798' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11798' class='GTTabs_curr'><a  id=\"11798_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11798' ><a  id=\"11798_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_11798'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<div id=\"attachment_11799\" style=\"width: 342px\" class=\"wp-caption alignright\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-11799\" data-attachment-id=\"11799\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11799\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6.png\" data-orig-size=\"553,285\" 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;}\" data-image-title=\"Gr\u00e1fico de f\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o $f$&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6.png\" class=\" wp-image-11799 \" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6.png\" alt=\"Representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o $f$\" width=\"332\" height=\"171\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6.png 553w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6-300x154.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6-150x77.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6-400x206.png 400w\" sizes=\"auto, (max-width: 332px) 100vw, 332px\" \/><\/a><p id=\"caption-attachment-11799\" class=\"wp-caption-text\">Representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o $f$<\/p><\/div>\n<p>Considere uma fun\u00e7\u00e3o $f$, real de vari\u00e1vel real, de dom\u00ednio $\\mathbb{R}$, cuja representa\u00e7\u00e3o gr\u00e1fica se apresenta ao lado.<\/p>\n<ol>\n<li>Complete a tabela:<br \/>\n<table style=\"width: 50%;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$x$<\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\"><\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\"><\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\"><\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$f\\left( x \\right)$<\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$0$<\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$1$<\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$3$<\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$5$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Determine a equa\u00e7\u00e3o reduzida de cada uma das retas: AB, BC e CD.<\/li>\n<li>Defina a fun\u00e7\u00e3o $f$ por ramos.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11798' onClick='GTTabs_show(1,11798)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11798'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>\n<div id=\"attachment_11799\" style=\"width: 342px\" class=\"wp-caption alignright\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-11799\" data-attachment-id=\"11799\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11799\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6.png\" data-orig-size=\"553,285\" 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;}\" data-image-title=\"Gr\u00e1fico de f\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o $f$&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6.png\" class=\" wp-image-11799 \" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6.png\" alt=\"Representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o $f$\" width=\"332\" height=\"171\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6.png 553w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6-300x154.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6-150x77.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2-pag116-6-400x206.png 400w\" sizes=\"auto, (max-width: 332px) 100vw, 332px\" \/><\/a><p id=\"caption-attachment-11799\" class=\"wp-caption-text\">Representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o $f$<\/p><\/div>\n<table style=\"width: 50%;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$x$<\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\"><span style=\"color: #000000;\">$\\begin{array}{*{20}{c}}<br \/>\n{x =\u00a0 &#8211; 2}&amp; \\vee &amp;{x = 6}<br \/>\n\\end{array}$<\/span><\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\"><span style=\"color: #000000;\">$\\begin{array}{*{20}{c}}<br \/>\n{x =\u00a0 &#8211; 1}&amp; \\vee &amp;{x = }<br \/>\n\\end{array}5$<\/span><\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\"><span style=\"color: #000000;\">$1 \\leqslant x \\leqslant 3$<\/span><\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\"><span style=\"color: #000000;\">$x \\in \\emptyset $<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$f\\left( x \\right)$<\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$0$<\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$1$<\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$3$<\/td>\n<td style=\"border: 1px solid #ff0000; width: 50px; text-align: center;\">$5$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Como o declive da reta AB \u00e9 ${m_{AB}} = 1$ e a ordenada na origem \u00e9 $b = 2$, ent\u00e3o $AB:y = x + 2$.\n<p>A equa\u00e7\u00e3o reduzida da reta BC \u00e9 $y = 3$.<\/p>\n<p>A equa\u00e7\u00e3o reduzida da reta CD \u00e9 da forma $y =\u00a0 &#8211; x + b$.<br \/>\nComo o ponto $C\\left( {3,3} \\right)$ pertence a esta reta, vem: $3 =\u00a0 &#8211; 3 + b \\Leftrightarrow b = 6$.<br \/>\nLogo, $CD:y =\u00a0 &#8211; x + 6$.<\/p>\n<\/li>\n<li>A fun\u00e7\u00e3o $f$ pode ser definida por:<br \/>\n\\[\\begin{array}{*{20}{c}}<br \/>\n{f\\left( x \\right)}&amp; = &amp;{\\left\\{ {\\begin{array}{*{20}{l}}<br \/>\n{x + 2}&amp; \\Leftarrow &amp;{x &lt; 1} \\\\<br \/>\n3&amp; \\Leftarrow &amp;{1 \\leqslant x \\leqslant 3} \\\\<br \/>\n{ &#8211; x + 6}&amp; \\Leftarrow &amp;{x &gt; 3}<br \/>\n\\end{array}} \\right.}<br \/>\n\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11798' onClick='GTTabs_show(0,11798)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considere uma fun\u00e7\u00e3o $f$, real de vari\u00e1vel real, de dom\u00ednio $\\mathbb{R}$, cuja representa\u00e7\u00e3o gr\u00e1fica se apresenta ao lado. Complete a tabela: $x$ $f\\left( x \\right)$ $0$ $1$ $3$ $5$ Determine a&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20879,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,133],"tags":[422,360,359],"series":[],"class_list":["post-11798","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcoes-definidas-por-ramos","tag-11-o-ano","tag-equacao-reduzida-da-reta","tag-funcao-definida-por-ramos"],"views":3531,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11V2Pag116-6_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11798","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=11798"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11798\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20879"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11798"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11798"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11798"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11798"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}