{"id":11769,"date":"2014-02-06T15:52:04","date_gmt":"2014-02-06T15:52:04","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11769"},"modified":"2022-01-22T01:46:52","modified_gmt":"2022-01-22T01:46:52","slug":"tres-funcoes-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11769","title":{"rendered":"Tr\u00eas fun\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_11769' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11769' class='GTTabs_curr'><a  id=\"11769_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11769' ><a  id=\"11769_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_11769'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<ol>\n<li>Represente graficamente, no mesmo referencial, as seguintes fun\u00e7\u00f5es:<br \/>\n\\[\\begin{array}{*{20}{r}}<br \/>\n{f\\left( x \\right) = x + 1}&amp;{\\text{;}}&amp;{g\\left( x \\right) = f\\left( {\\frac{1}{x}} \\right)}&amp;{\\text{e}}&amp;{h\\left( x \\right) = \\frac{1}{{f\\left( x \\right)}}}<br \/>\n\\end{array}\\]<\/li>\n<li>Determine o dom\u00ednio de cada uma das fun\u00e7\u00f5es anteriores.<\/li>\n<li>Compare os tr\u00eas gr\u00e1ficos.<br \/>\nQuais os pontos dos gr\u00e1ficos de $g$ e de $h$ que se mant\u00eam invariantes relativamente ao gr\u00e1fico de $f$?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11769' onClick='GTTabs_show(1,11769)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11769'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>\\[\\begin{array}{*{20}{r}}<br \/>\n{f\\left( x \\right) = x + 1}&amp;{\\text{;}}&amp;{g\\left( x \\right) = f\\left( {\\frac{1}{x}} \\right) = \\frac{1}{x} + 1}&amp;{\\text{e}}&amp;{h\\left( x \\right) = \\frac{1}{{f\\left( x \\right)}} = \\frac{1}{{x + 1}}}<br \/>\n\\end{array}\\]<\/p>\n<div id=\"attachment_11770\" style=\"width: 629px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-51-9.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-11770\" data-attachment-id=\"11770\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11770\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-51-9.png\" data-orig-size=\"884,582\" 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\u00e1ficos\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Representa\u00e7\u00e3o gr\u00e1fica das fun\u00e7\u00f5es $f$, $g$ e $h$&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-51-9.png\" class=\" wp-image-11770 \" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-51-9.png\" alt=\"Representa\u00e7\u00e3o gr\u00e1fica das fun\u00e7\u00f5es $f$, $g$ e $h$\" width=\"619\" height=\"407\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-51-9.png 884w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-51-9-300x197.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-51-9-150x98.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-51-9-400x263.png 400w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/a><p id=\"caption-attachment-11770\" class=\"wp-caption-text\">Representa\u00e7\u00e3o gr\u00e1fica das fun\u00e7\u00f5es $f$, $g$ e $h$<\/p><\/div>\n<p>\u00ad<\/p>\n<\/li>\n<li>\\[{D_f} = \\left\\{ {x \\in \\mathbb{R}:\\left( {x + 1} \\right) \\in \\mathbb{R}} \\right\\} = \\mathbb{R}\\]<br \/>\n\\[{D_g} = \\left\\{ {x \\in \\mathbb{R}:\\left( {\\frac{1}{x} + 1} \\right) \\in \\mathbb{R}} \\right\\} = \\left\\{ {x \\in \\mathbb{R}:x \\ne 0} \\right\\} = \\mathbb{R}\\backslash \\left\\{ 0 \\right\\}\\]<br \/>\n\\[{D_h} = \\left\\{ {x \\in \\mathbb{R}:\\left( {\\frac{1}{{x + 1}}} \\right) \\in \\mathbb{R}} \\right\\} = \\left\\{ {x \\in \\mathbb{R}:x + 1 \\ne 0} \\right\\} = \\mathbb{R}\\backslash \\left\\{ { &#8211; 1} \\right\\}\\]<br \/>\n\u00ad<\/li>\n<li>Os pontos $A\\left( { &#8211; 1,0} \\right)$ e $B\\left( {1,2} \\right)$, do gr\u00e1fico de $g$,\u00a0s\u00e3o invariantes relativamente ao gr\u00e1fico de $f$.\n<p>Os pontos $C\\left( { &#8211; 2, &#8211; 1} \\right)$ e $D\\left( {0,1} \\right)$, do gr\u00e1fico de $h$, s\u00e3o invariantes relativamente ao gr\u00e1fico de $f$.<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11769' onClick='GTTabs_show(0,11769)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Represente graficamente, no mesmo referencial, as seguintes fun\u00e7\u00f5es: \\[\\begin{array}{*{20}{r}} {f\\left( x \\right) = x + 1}&amp;{\\text{;}}&amp;{g\\left( x \\right) = f\\left( {\\frac{1}{x}} \\right)}&amp;{\\text{e}}&amp;{h\\left( x \\right) = \\frac{1}{{f\\left( x \\right)}}} \\end{array}\\] Determine o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20875,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,125],"tags":[422,126],"series":[],"class_list":["post-11769","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcoes-racionais","tag-11-o-ano","tag-funcao-racional"],"views":2142,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11V2Pag051-9_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11769","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=11769"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11769\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20875"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11769"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11769"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11769"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11769"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}