{"id":11737,"date":"2014-02-03T10:33:12","date_gmt":"2014-02-03T10:33:12","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11737"},"modified":"2022-01-14T18:54:46","modified_gmt":"2022-01-14T18:54:46","slug":"considere-a-funcao-g","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11737","title":{"rendered":"Considere a fun\u00e7\u00e3o $g$"},"content":{"rendered":"<p><ul id='GTTabs_ul_11737' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11737' class='GTTabs_curr'><a  id=\"11737_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11737' ><a  id=\"11737_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_11737'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considere a fun\u00e7\u00e3o $g$, definida por: \\[g\\left( x \\right) = 5 + \\frac{2}{{x &#8211; 3}}\\]<\/p>\n<ol>\n<li>Esboce o gr\u00e1fico de $g$.<\/li>\n<li>Indique como se obt\u00e9m, por meio de uma s\u00e9rie de transforma\u00e7\u00f5es geom\u00e9tricas, o gr\u00e1fico da fun\u00e7\u00e3o $g$, a partir do gr\u00e1fico da fun\u00e7\u00e3o $f\\left( x \\right) = \\frac{1}{x}$.<\/li>\n<li>Resolva graficamente a inequa\u00e7\u00e3o $g\\left( x \\right) &gt; 1$.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11737' onClick='GTTabs_show(1,11737)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11737'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>\n<p>Desenhadas as ass\u00edntotas do gr\u00e1fico de $g$, construiu-se uma tabela de valores da fun\u00e7\u00e3o e representaram-se os pontos correspondentes. Finalmente, esbo\u00e7ou-se o gr\u00e1fico da fun\u00e7\u00e3o.<\/p>\n<p><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":768,\r\n\"height\":548,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 59 || 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 || 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 || 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ 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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><\/p>\n<\/li>\n<li>O gr\u00e1fico de $g$ pode ser obtido do gr\u00e1fico de $f$ atrav\u00e9s da seguinte sequ\u00eancia de transforma\u00e7\u00f5es:\n<p>&#8211; obten\u00e7\u00e3o do gr\u00e1fico de $p$, por dila\u00e7\u00e3o do gr\u00e1fico de $g$ em rela\u00e7\u00e3o ao eixo $Oy$ com fator 2;<\/p>\n<p>&#8211; obten\u00e7\u00e3o do gr\u00e1fico de $q$ por transla\u00e7\u00e3o do gr\u00e1fico de $p$, associada ao vetor de coordenadas $\\left( {3,0} \\right)$;<\/p>\n<p>&#8211; finalmente, obten\u00e7\u00e3o do gr\u00e1fico de $g$ por transla\u00e7\u00e3o do gr\u00e1fico de $q$, associada ao vetor de coordenadas $\\left( {0,5} \\right)$.<\/p>\n<p>(Ver anima\u00e7\u00e3o abaixo.)<\/p>\n<\/li>\n<li>A resolu\u00e7\u00e3o gr\u00e1fica da condi\u00e7\u00e3o $g\\left( x \\right) &gt; 1$ permite concluir: \\[g\\left( x \\right) &gt; 1 \\Leftrightarrow x \\in \\left] { &#8211; \\infty ,\\frac{5}{2}} \\right[ \\cup \\left] {3, + \\infty } \\right[\\]<br \/>\n(Ver anima\u00e7\u00e3o abaixo.)<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><div id=\"ggbApplet2\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet2\",\r\n\"width\":885,\r\n\"height\":557,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 59 || 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 || 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 || 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ 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