{"id":25057,"date":"2023-04-14T18:28:32","date_gmt":"2023-04-14T17:28:32","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25057"},"modified":"2023-04-22T17:03:55","modified_gmt":"2023-04-22T16:03:55","slug":"duas-funcoes-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25057","title":{"rendered":"Duas fun\u00e7\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25057' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25057' class='GTTabs_curr'><a  id=\"25057_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25057' ><a  id=\"25057_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_25057'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera as fun\u00e7\u00f5es <em>f<\/em> e <em>g<\/em> definidas, respetivamente, por:<\/p>\n<p>\\[\\begin{array}{*{20}{c}}{f\\left( x \\right) = 2x + 1}&amp;{\\rm{e}}&amp;{g\\left( x \\right) = &#8211; 2x + 3}\\end{array}\\]<\/p>\n<ol>\n<li>Qual \u00e9 o objeto cuja imagem pela fun\u00e7\u00e3o <em>f<\/em> \u00e9 13?<\/li>\n<li>Qual \u00e9 a imagem do objeto 0 por cada uma das fun\u00e7\u00f5es? E do objeto \u22121?<\/li>\n<li>Em que ponto o gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em> interseta o eixo <em>yy<\/em>? E o eixo <em>xx<\/em>?<br \/>E a fun\u00e7\u00e3o <em>g<\/em>?<\/li>\n<li>Representa graficamente as fun\u00e7\u00f5es <em>f<\/em> e <em>g<\/em>.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25057' onClick='GTTabs_show(1,25057)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25057'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><\/p>\n<blockquote>\n<p>Considera as fun\u00e7\u00f5es <em>f<\/em> e <em>g<\/em> definidas, respetivamente, por:<\/p>\n<\/blockquote>\n<p>\\[\\begin{array}{*{20}{c}}{f\\left( x \\right) = 2x + 1}&amp;{\\rm{e}}&amp;{g\\left( x \\right) = &#8211; 2x + 3}\\end{array}\\]<br \/><br \/><\/p>\n<ol>\n<li>\u00c9 6 o objeto cuja imagem pela fun\u00e7\u00e3o <em>f<\/em> \u00e9 13, pois:<br \/>\\[\\begin{array}{*{20}{l}}{f\\left( x \\right) = 13}&amp; \\Leftrightarrow &amp;{2x + 1 = 13}\\\\{}&amp; \\Leftrightarrow &amp;{2x = 12}\\\\{}&amp; \\Leftrightarrow &amp;{x = 6}\\end{array}\\]<\/li>\n<li>As imagens do objeto 0 por cada uma das fun\u00e7\u00f5es s\u00e3o: \\(f\\left( 0 \\right) = 2 \\times 0 + 1 = 1\\) e \\(g\\left( 0 \\right) = &#8211; 2 \\times 0 + 3 = 3\\).<br \/>As do objeto \u22121 \u00a0s\u00e3o: \\(f\\left( { &#8211; 1} \\right) = 2 \\times \\left( { &#8211; 1} \\right) + 1 = &#8211; 1\\) e \\(g\\left( { &#8211; 1} \\right) = &#8211; 2 \\times \\left( { &#8211; 1} \\right) + 3 = 5\\).<br \/><br \/><\/li>\n<li>Note-se que qualquer ponto do eixo <em>yy<\/em> tem <span style=\"text-decoration: underline;\">abcissa nula<\/span>.<br \/>Note-se que qualquer ponto do eixo <em>xx<\/em> tem <span style=\"text-decoration: underline;\">ordenada nula<\/span>.<br \/>O gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em> interseta o eixo <em>yy<\/em> no ponto de coordenadas \\(\\left( {0,\\,1} \\right)\\), pois \\(f\\left( 0 \\right) = 2 \\times 0 + 1 = 1\\).<br \/>O gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em> interseta o eixo <em>yy<\/em> no ponto de coordenadas \\(\\left( {0,\\,3} \\right)\\), pois \\(g\\left( 0 \\right) = &#8211; 2 \\times 0 + 3 = 3\\).<br \/>Os gr\u00e1ficos de <em>f<\/em> e <em>g<\/em> intersetam o eixo <em>xx<\/em>, respetivamente, nos pontos de coordenadas \\(\\left( { &#8211; \\frac{1}{2},\\,0} \\right)\\) e \\(\\left( {\\frac{3}{2},\\,0} \\right)\\):<br \/>\\[\\begin{array}{*{20}{c}}{\\begin{array}{*{20}{l}}{f\\left( x \\right) = 0}&amp; \\Leftrightarrow &amp;{2x + 1 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{2x = &#8211; 1}\\\\{}&amp; \\Leftrightarrow &amp;{x = &#8211; \\frac{1}{2}}\\end{array}}&amp;{}&amp;{\\begin{array}{*{20}{l}}{g\\left( x \\right) = 0}&amp; \\Leftrightarrow &amp;{ &#8211; 2x + 3 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; 2x = &#8211; 3}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{3}{2}}\\end{array}}\\end{array}\\]<\/li>\n<li>Segue uma representa\u00e7\u00e3o gr\u00e1fica das fun\u00e7\u00f5es <em>f<\/em> e <em>g<\/em>:<br \/><br \/><\/li>\n<\/ol>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag169-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25067\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25067\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag169-3.png\" data-orig-size=\"670,586\" 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=\"8_Pag169-3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag169-3.png\" class=\"aligncenter wp-image-25067\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag169-3-300x262.png\" alt=\"\" width=\"520\" height=\"455\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag169-3-300x262.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag169-3.png 670w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/a><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25057' onClick='GTTabs_show(0,25057)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera as fun\u00e7\u00f5es f e g definidas, respetivamente, por: \\[\\begin{array}{*{20}{c}}{f\\left( x \\right) = 2x + 1}&amp;{\\rm{e}}&amp;{g\\left( x \\right) = &#8211; 2x + 3}\\end{array}\\] Qual \u00e9 o objeto cuja imagem pela fun\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":25079,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,709],"tags":[424,345,344],"series":[],"class_list":["post-25057","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-graficos-de-funcoes-afins","tag-8-o-ano","tag-funcao-afim","tag-grafico"],"views":129,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag169-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25057","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=25057"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25057\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25079"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25057"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25057"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25057"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25057"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}