{"id":2128,"date":"2016-12-04T22:30:35","date_gmt":"2016-12-04T21:30:35","guid":{"rendered":"http:\/\/mathsguyon.fr\/?page_id=2128"},"modified":"2024-05-12T15:30:59","modified_gmt":"2024-05-12T14:30:59","slug":"fonctions-affines-et-problemes-du-premier-degre","status":"publish","type":"page","link":"https:\/\/mathsguyon.fr\/?page_id=2128","title":{"rendered":"20. Fonctions Affines"},"content":{"rendered":"<h1 style=\"text-align: center;\">\u00a0\u00a0 \u00a0 <a href=\"http:\/\/mathsguyon.fr\/wp-content\/uploads\/2024\/05\/Cours_fonctions_affines_2024.pdf\">Cours<\/a>\u00a0\u00a0\u00a0\u00a0<a href=\"http:\/\/mathsguyon.fr\/wp-content\/uploads\/2024\/05\/Parcours_FonctionsAffines_2024_enonce.pdf\">Plan de Travail<\/a><\/h1>\n<h1 style=\"text-align: center;\">Le cours en vid\u00e9o<\/h1>\n<hr \/>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #800000;\">D\u00e9finitions des fonctions affines<\/span><\/strong><\/h2>\n<h2 style=\"text-align: center;\"><a href=\"https:\/\/youtube.com\/embed\/1iOhyUnZ0tU\">Vid\u00e9o 1<\/a>\u00a0 &#8211; <span style=\"color: #800000;\">QCM n\u00b01<\/span> :<a href=\"https:\/\/link.dgpad.net\/1Knj\"> identifi\u00e9<\/a> &#8211;\u00a0 anonymes\u00a0 ;<\/h2>\n<h2 style=\"text-align: center;\"><span style=\"color: #800000;\">QCM n\u00b02\u00a0<\/span> \u00a0 <a href=\"https:\/\/link.dgpad.net\/VWbm\">identifi\u00e9<\/a> &#8211;\u00a0 \u00a0 anonymes<\/h2>\n<p><strong>Exercice 1 :<span style=\"color: #008000;\"> <a style=\"color: #008000;\" href=\"http:\/\/mathsguyon.fr\/wp-content\/uploads\/2016\/12\/reconnaitre-fct-affine-corrige.pdf\">Correction en pdf<\/a><\/span><br \/>\n<\/strong><\/p>\n<p>Dire si les fonctions suivantes sont affines ou non :<\/p>\n<p>\\(~f(x) = \\dfrac{1}{2}x+3~\\) ; \u00a0\\(~g(x) = 1 &#8211; x~\\) ; \\(~f(x)=3x^2~\\) ; \\(~k(x)=\\dfrac{2x+3}{5}~\\); \\(~l(x)=\\dfrac{x}{2}~\\)<\/p>\n<hr \/>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #800000;\">Propri\u00e9t\u00e9 des fonctions affines<\/span><\/strong><\/h2>\n<h2 style=\"text-align: center;\"><a href=\"https:\/\/youtube.com\/embed\/3Ba49f9ZafQ\">Vid\u00e9o 2 :<\/a>\u00a0 + <span style=\"color: #800000;\">QCM n\u00b03<\/span> \u00a0\u00a0 <a href=\"https:\/\/link.dgpad.net\/DFtw\"> identifi\u00e9<\/a> &#8211;\u00a0 anonymes<\/h2>\n<p><strong>Exercice 2 :<\/strong><\/p>\n<ul>\n<li>D\u00e9terminer la fonction affine \\(f\\) qui v\u00e9rifie \\(f(3)=2\\) et \\(f(1)=-2\\) <strong><a href=\"http:\/\/mathsguyon.fr\/wp-content\/uploads\/2016\/12\/determiner-a-et-b.pdf\"><span style=\"color: #008000;\">Correction en pdf<\/span><\/a><\/strong><\/li>\n<li>D\u00e9terminer la fonction affine \\(f\\) qui v\u00e9rifie \\(f(-1)=5\\) et \\(f(2)=1\\)\u00a0 <strong><a href=\"https:\/\/youtube.com\/embed\/KWRdA5oMpXk\"><span style=\"color: #008000;\">Correction en vid\u00e9o<\/span><\/a><\/strong><br \/>\n<hr \/>\n<\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #800000;\">Repr\u00e9sentation graphique d&rsquo;une fonction affine<\/span><\/strong><\/h2>\n<h2 style=\"text-align: center;\"><a href=\"https:\/\/youtube.com\/embed\/UZJwaAzc0e4\">Vid\u00e9o 3<\/a><\/h2>\n<h2 style=\"text-align: center;\"><span style=\"color: #800000;\">QCM n\u00b04<\/span> : <a href=\"https:\/\/link.dgpad.net\/yoQg\">Identifi\u00e9\u00a0<\/a> &#8211; Anonymes \u00a0\u00a0\u00a0 et <span style=\"color: #800000;\">QCM n\u00b05<\/span><span style=\"color: #800000;\">\u00a0 :\u00a0\u00a0 <\/span><a href=\"https:\/\/link.dgpad.net\/jBGf\">Identifi\u00e9\u00a0<\/a> &#8211; Anonymes<\/h2>\n<h2 style=\"text-align: center;\"><span style=\"color: #800000;\">\u00a0 <\/span><\/h2>\n<p><strong>Exercice 3 : <a href=\"http:\/\/mathsguyon.fr\/wp-content\/uploads\/2016\/12\/reprsenter-graphiquement-corrige.pdf\"><span style=\"color: #008000;\">correction en pdf<\/span><\/a><br \/>\n<\/strong><\/p>\n<p>Repr\u00e9senter graphiquement la fonction affine \\(f\\) d\u00e9finie par \\(f(x) = 2 x +3\\) &#8211;<\/p>\n<p><strong>Exercice 4 : <\/strong>\u00a0 <strong><span style=\"color: #008000;\"><a style=\"color: #008000;\" href=\"http:\/\/mathsguyon.fr\/wp-content\/uploads\/2016\/12\/intersection-droites-corrig\u00e9-1.pdf\">Correction en pdf<\/a><\/span><\/strong><\/p>\n<p>On consid\u00e8re les fonctions affines \\(f\\) et \\(g\\) d\u00e9finie sur \\(\\mathbb{R}\\) par \\(f(x) = x+2\\) et \\(g(x) = 3 x -2\\)<\/p>\n<p>On appelle \\((d_1)\\) la droite repr\u00e9sentative de \\(f\\) et \\((d_2)\\) la droite repr\u00e9sentative de \\(g\\)<\/p>\n<ol>\n<li>D\u00e9terminer les coordonn\u00e9es du point d&rsquo;intersection de \\((d_1)\\) et \\((d_2)\\)<\/li>\n<li>D\u00e9terminer les positions relatives de deux droites<\/li>\n<\/ol>\n<hr \/>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #800000;\">D\u00e9termination graphique de \\(a\\) et \\(b\\)<\/span><\/strong><\/h2>\n<h2 style=\"text-align: center;\"><a href=\"https:\/\/youtube.com\/embed\/7eZWAJ3q3jE\">Vid\u00e9o 4<\/a> :\u00a0\u00a0\u00a0 +<span style=\"color: #800000;\"> QCM n\u00b06 : <a href=\"https:\/\/link.dgpad.net\/qsEb\">Identifi\u00e9<\/a> &#8211; Anonymes<\/span><\/h2>\n<p><strong>\u00a0<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-7663 alignright\" src=\"http:\/\/mathsguyon.fr\/wp-content\/uploads\/2020\/05\/aetb.png\" alt=\"\" width=\"354\" height=\"258\" srcset=\"https:\/\/mathsguyon.fr\/wp-content\/uploads\/2020\/05\/aetb.png 584w, https:\/\/mathsguyon.fr\/wp-content\/uploads\/2020\/05\/aetb-300x219.png 300w\" sizes=\"auto, (max-width: 354px) 100vw, 354px\" \/><strong>Exercice 5 : <\/strong>\u00a0 <span style=\"color: #008000;\"><a style=\"color: #008000;\" href=\"http:\/\/mathsguyon.fr\/?page_id=7667\"><strong>Correction \u00e9crite<\/strong><\/a><\/span><\/p>\n<p>On consid\u00e8re les fonctions affines :<\/p>\n<p>\\(f_1\\) repr\u00e9sent\u00e9e en rouge, \\(f_2\\) repr\u00e9sent\u00e9e en bleu ciel, \\(f_3\\) repr\u00e9sent\u00e9e en vert, \\(f_4\\) repr\u00e9sent\u00e9e en bleu marine et \\(f_5\\) repr\u00e9sent\u00e9e en orange dans le rep\u00e8re ci-dessous.<\/p>\n<p>D\u00e9terminer les expressions de chacune de ces fonctions.<\/p>\n<hr \/>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #800000;\">Fonction affine : sens de variation<\/span><\/strong><\/h2>\n<h2 style=\"text-align: center;\"><a href=\"https:\/\/youtube.com\/embed\/tdagLKx1mUU\">Vid\u00e9o 5 :<\/a> \u00a0\u00a0\u00a0 + <span style=\"color: #800000;\">QCM n\u00b07\u00a0 : <a href=\"https:\/\/link.dgpad.net\/wS1K\">Identifi\u00e9\u00a0<\/a> &#8211;\u00a0 Anonymes<\/span><\/h2>\n<p><strong>Exercice 6 :\u00a0\u00a0<span style=\"color: #008000;\"> <a style=\"color: #008000;\" href=\"https:\/\/youtube.com\/embed\/zZptDRiueF8\">Correction en vid\u00e9o<\/a><\/span><\/strong><\/p>\n<p>Donner le sens de variation de la fonction \\(f\\) d\u00e9finie sur \\(\\mathbb{R}\\) par \\(f(x) = 2 x-3\\) .<\/p>\n<p><strong>Exercice 7 :\u00a0\u00a0<a href=\"http:\/\/mathsguyon.fr\/wp-content\/uploads\/2016\/12\/sens-variation-corrige.pdf\"><span style=\"color: #008000;\"> Correction en pdf<\/span><\/a><\/strong><\/p>\n<p>Donner le sens de variation de la fonction \\(g\\) d\u00e9finie sur \\(\\mathbb{R}\\) par \\(g(x) = 5-3 x\\) .<\/p>\n<p><strong>Exercice 8 : \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<span style=\"color: #008000;\"> <a style=\"color: #008000;\" href=\"http:\/\/mathsguyon.fr\/wp-content\/uploads\/2016\/12\/sens-variation-corrige.pdf\">Correction en pdf<\/a><\/span><\/strong><\/p>\n<p>Donner le sens de variation de la fonction \\(f\\) d\u00e9finie sur \\(\\mathbb{R}\\) par \\(f(x) = -2x+4\\) puis le signe de \\(f(x)\\).<\/p>\n<p><strong>Exercice 9 :\u00a0 <span style=\"color: #008000;\">\u00a0 <a style=\"color: #008000;\" href=\"http:\/\/mathsguyon.fr\/wp-content\/uploads\/2016\/12\/sens-de-variation-corr3-1.pdf\">Correction en pdf<\/a><\/span><\/strong><\/p>\n<p>1.\u00a0 Donner le sens de variation de la fonction \\(f\\) d\u00e9finie sur \\(\\mathbb{R}\\) par \\(f(x) = -x+3\\) puis tracer la repr\u00e9sentation graphique de \\(f\\).<\/p>\n<p>2. Peut-on comparer, sans calcul \\(- \\sqrt{2}+3\\) et \\(- \\sqrt{3}+3\\)<\/p>\n<p><strong>Exercice 10 :\u00a0\u00a0 <span style=\"color: #008000;\"><a style=\"color: #008000;\" href=\"http:\/\/mathsguyon.fr\/wp-content\/uploads\/2016\/12\/sens-de-variation-corrig\u00e92.pdf\">Correction en pdf<\/a><\/span><\/strong><\/p>\n<p>Donner le sens de variation des fonction \\(f\\) et \\(g\\) d\u00e9finies sur \\(\\mathbb{R}\\) par \\(f(x) = -x+2\\) et \\(g(x) = 2x\\)<\/p>\n<p>puis tracer leur repr\u00e9sentation graphique dans le m\u00eame rep\u00e8re.<\/p>\n<hr \/>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #800000;\">Fonctions affines : signe d&rsquo;une fonction affine<\/span><\/strong><\/h2>\n<h2 style=\"text-align: center;\"><a href=\"https:\/\/youtube.com\/embed\/vRI03ajXRac\">Vid\u00e9o 6<\/a> \u00a0\u00a0 &#8211;\u00a0<a href=\"https:\/\/youtube.com\/embed\/lb_ISW5RU8A\">Vid\u00e9o 7<\/a><\/h2>\n<h2 style=\"text-align: center;\">\u00a0 QCM 8 : <a href=\"https:\/\/doctools.dgpad.net\/connect.php?datas=eyJiYXNlaWQiOiIxMEllUkF1c2ZQSmdSejcxd0tiMThGeGJJRVA0aWVkVTRXck4xZDVYS3pIRSIsImRlX2Jhc2UiOiIxWF9MaGlYSDZadW43dHJTQVZZdjYxbUkzU194X1o5RXFEM1BSZkVjN19wQSIsImlkIjoiMUNfTTZZc0xNOVlMakhGeUVKaElnc05TYkh5dzJCZXlDNmlCVW9UTFdGN2siLCJ1c2VycyI6IkFub255bWUifQ==\">Identifi\u00e9\u00a0<\/a> &#8211; <a href=\"https:\/\/doctools.dgpad.net\/exam.php?datas=eyJiYXNlaWQiOiIxMEllUkF1c2ZQSmdSejcxd0tiMThGeGJJRVA0aWVkVTRXck4xZDVYS3pIRSIsImRlX2Jhc2UiOiIxWF9MaGlYSDZadW43dHJTQVZZdjYxbUkzU194X1o5RXFEM1BSZkVjN19wQSIsImlkIjoiMXFIeGZJQXA4M3RhYnNKLVRGYmpOTWJHTFdBQ1FMOEQyOVhJc3k0eGw0d0UiLCJ1c2VycyI6IkFub255bWUifQ==\">Anonyme<\/a><\/h2>\n<p><strong>Exercice\u00a0 11 :\u00a0 <a href=\"https:\/\/youtube.com\/embed\/UNpegQsgbWs\">Correction en vid\u00e9o<\/a><br \/>\n<\/strong><\/p>\n<p>D\u00e9terminer le signe de la fonction \\(g\\) d\u00e9finie sur\u00a0 \\(\\mathbb{R}\\) par \\(g( x )=4-3x\\)<\/p>\n<p><strong>Exercice\u00a0 12 : <a href=\"https:\/\/youtube.com\/embed\/kg0vnYWtf-4\">Correction en vid\u00e9o<\/a><br \/>\n<\/strong><\/p>\n<p>D\u00e9terminer le signe de la fonction \\(v\\) d\u00e9finie sur\u00a0 \\(\\mathbb{R}\\) par \\(v( x )=(1- \\sqrt2) x + \\sqrt3\\)<\/p>\n<p><strong>Exercice 13 :\u00a0\u00a0 <\/strong><span style=\"color: #008000;\"><a style=\"color: #008000;\" href=\"http:\/\/mathsguyon.fr\/?page_id=7679\"><strong>Correction \u00e9crite<\/strong><\/a><\/span><\/p>\n<p>D\u00e9terminer le signe de la fonction \\f\\) d\u00e9finie sur \\(\\mathbb{R}\\) par \\(f(x) = &#8211; 2 x + 5\\)<\/p>\n<hr \/>\n<h2 style=\"text-align: center;\"><span style=\"color: #800000;\"><strong>R\u00e9soudre une in\u00e9quation avec un tableau de signes<\/strong><\/span><\/h2>\n<h2 style=\"text-align: center;\">R\u00e9soudre dans \\(\\mathbb{R}\\) : \\((4x+1)(3-x)\\geq 0\\) :\u00a0 <a href=\"https:\/\/youtube.com\/embed\/wBKzwRjLIek\">Vid\u00e9o 8<\/a> \u00a0 &#8211;<\/h2>\n<p><strong>Exercice 14 :\u00a0 <\/strong><\/p>\n<p>R\u00e9soudre dans \\(\\mathbb{R}\\) : \\(( 5 x-1)(-2 x+1)&gt; 0\\) <a href=\"https:\/\/www.dropbox.com\/s\/174xnk1wr66ajjm\/exo13_corr.pdf?dl=0\"> Correction \u00e9crite<\/a><\/p>\n<hr \/>\n<h2 style=\"text-align: center;\"><span style=\"color: #800000;\"><strong>\u00c9tude du signe d&rsquo;une expression avec un tableau de signe<\/strong><\/span><\/h2>\n<h2 style=\"text-align: center;\"><a href=\"https:\/\/youtube.com\/embed\/Yl2rz6wvk1M?rel=0\">Vid\u00e9o 9<\/a> \u00a0\u00a0 &#8211;<\/h2>\n<p style=\"text-align: left;\"><strong>Exercice 15 : <span style=\"color: #008000;\"><a style=\"color: #008000;\" href=\"http:\/\/mathsguyon.fr\/?page_id=7715\">Correction \u00e9crite<\/a><\/span><br \/>\n<\/strong><\/p>\n<p>R\u00e9soudre dans \\(\\mathbb{R}\\) les in\u00e9quations suivantes :<\/p>\n<p>\\((3x-2)^2-(x+1)^2\\geq 0\\)<\/p>\n<hr \/>\n<h1 style=\"text-align: center;\"><strong><a href=\"https:\/\/mathsguyon.fr\/test\/index.php?l=fr&amp;n=2e&amp;c=exercices#IX\">Exercices corrig\u00e9s en vid\u00e9os pour r\u00e9viser<\/a><br \/>\n<\/strong><\/h1>\n<h2><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0\u00a0 \u00a0 Cours\u00a0\u00a0\u00a0\u00a0Plan de Travail Le cours en vid\u00e9o D\u00e9finitions des fonctions affines Vid\u00e9o 1\u00a0 &#8211; QCM n\u00b01 : identifi\u00e9 &#8211;\u00a0 anonymes\u00a0 ; QCM n\u00b02\u00a0 \u00a0 identifi\u00e9 &#8211;\u00a0 \u00a0 anonymes Exercice 1 : Correction en pdf Dire si les fonctions &hellip; <a href=\"https:\/\/mathsguyon.fr\/?page_id=2128\">Continuer la lecture <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":21,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2128","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/2128","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2128"}],"version-history":[{"count":106,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/2128\/revisions"}],"predecessor-version":[{"id":9564,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/2128\/revisions\/9564"}],"up":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/21"}],"wp:attachment":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}