{"id":25428,"date":"2023-04-23T23:31:34","date_gmt":"2023-04-23T22:31:34","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25428"},"modified":"2023-05-05T15:06:20","modified_gmt":"2023-05-05T14:06:20","slug":"qual-e-outro-ponto-do-grafico","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25428","title":{"rendered":"Qual \u00e9 outro ponto do gr\u00e1fico?"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25428' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25428' class='GTTabs_curr'><a  id=\"25428_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25428' ><a  id=\"25428_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_25428'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Se os pontos \\(\\left( { &#8211; 1,4} \\right)\\) e \\(\\left( {3,0} \\right)\\) pertencem ao gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em> definida por \\(f\\left( x \\right) = ax + b\\), um outro ponto desse gr\u00e1fico \u00e9:<\/p>\n<p><strong>[A]<\/strong> \\(\\left( {1,2} \\right)\\)<br \/><strong>[B]<\/strong> \\(\\left( {1,4} \\right)\\)<br \/><strong>[C]<\/strong> \\(\\left( {3,6} \\right)\\)<br \/><strong>[D]<\/strong> \\(\\left( { &#8211; 3,2} \\right)\\)<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25428' onClick='GTTabs_show(1,25428)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25428'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Se os pontos \\(\\left( { &#8211; 1,4} \\right)\\) e \\(\\left( {3,0} \\right)\\) pertencem ao gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em> definida por \\(f\\left( x \\right) = ax + b\\), um outro ponto desse gr\u00e1fico \u00e9:<\/p>\n<p><strong>[A]<\/strong> \\(\\left( {1,2} \\right)\\)<br \/><strong>[B]<\/strong> \\(\\left( {1,4} \\right)\\)<br \/><strong>[C]<\/strong> \\(\\left( {3,6} \\right)\\)<br \/><strong>[D]<\/strong> \\(\\left( { &#8211; 3,2} \\right)\\)<\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<p>A reta que \u00e9 o gr\u00e1fico da fun\u00e7\u00e3o tem declive \\(a = \\frac{{4 &#8211; 0}}{{ &#8211; 1 &#8211; 3}} = &#8211; 1\\).<br \/>Logo, a express\u00e3o alg\u00e9brica da fun\u00e7\u00e3o \u00e9 do tipo \\(f\\left( x \\right) = &#8211; x + b\\).<br \/>Como \\(f\\left( { &#8211; 1} \\right) = 4\\), vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{f\\left( { &#8211; 1} \\right) = 4}&amp; \\Leftrightarrow &amp;{ &#8211; \\left( { &#8211; 1} \\right) + b = 4}\\\\{}&amp; \\Leftrightarrow &amp;{b = 3}\\end{array}\\]<\/p>\n<p>Assim, uma express\u00e3o alg\u00e9brica da fun\u00e7\u00e3o <em>f<\/em> \u00e9 \\(f\\left( x \\right) = &#8211; x + 3\\).<\/p>\n<p>A op\u00e7\u00e3o correta \u00e9 <strong>[A]<\/strong> \\(\\left( {1,2} \\right)\\), pois \\(f\\left( 1 \\right) = 2\\).<\/p>\n<p>\u00a0<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag179-9_graf.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25437\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25437\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag179-9_graf.png\" data-orig-size=\"1296,933\" 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_Pag179-9_graf\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag179-9_graf-1024x737.png\" class=\"aligncenter wp-image-25437\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag179-9_graf-300x216.png\" alt=\"\" width=\"520\" height=\"374\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag179-9_graf-300x216.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag179-9_graf-1024x737.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag179-9_graf-768x553.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag179-9_graf.png 1296w\" 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_25428' onClick='GTTabs_show(0,25428)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Se os pontos \\(\\left( { &#8211; 1,4} \\right)\\) e \\(\\left( {3,0} \\right)\\) pertencem ao gr\u00e1fico da fun\u00e7\u00e3o f definida por \\(f\\left( x \\right) = ax + b\\), um outro ponto desse&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":25439,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,709],"tags":[424,346,345,344],"series":[],"class_list":["post-25428","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-declive","tag-funcao-afim","tag-grafico"],"views":75,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag179-9_graf_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25428","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=25428"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25428\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25439"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25428"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25428"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25428"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25428"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}