{"id":2771,"date":"2020-02-13T08:20:16","date_gmt":"2020-02-13T07:20:16","guid":{"rendered":"http:\/\/jhmaths.fr\/?page_id=2771"},"modified":"2021-05-10T10:21:29","modified_gmt":"2021-05-10T08:21:29","slug":"fonctions-affines","status":"publish","type":"page","link":"https:\/\/jhmaths.fr\/index.php\/seconde\/fonctions-affines\/","title":{"rendered":"Fonctions affines"},"content":{"rendered":"<p>[vc_row][vc_column][vc_column_text el_id=\u00a0\u00bbobjectif-1&Prime;]<\/p>\n<h1 style=\"text-align: center;\">D\u00e9finition<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<span class=\"proprieteseconde\">Une fonction affine s&rsquo;\u00e9crit \\(f(x)=mx+p\\)<\/span><\/p>\n<p><span class=\"proprieteseconde\">\\(m\\) s&rsquo;appelle le coefficient directeur.<\/span><\/p>\n<p><span class=\"proprieteseconde\">\\(p\\) s&rsquo;appelle l&rsquo;ordonn\u00e9e \u00e0 l&rsquo;origine.<\/span>[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<\/p>\n<h3><span class=\"proprieteseconde\">Taux d&rsquo;accroissement <\/span><\/h3>\n<p><span class=\"proprieteseconde\">Dans le cas des fonctions affines, le taux d&rsquo;accroissement \\(\\displaystyle \\frac{f(b)-f(a)}{b-a}\\) est constant (et \u00e9gal \u00e0 \\(m\\) )<\/span>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text]<\/p>\n<div style=\"text-align: center;\"><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/0jX7iPWCWI4\" width=\"320\" height=\"180\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/div>\n<p>[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<span class=\"proprieteseconde\">Si \\(p=0\\) (c&rsquo;est-\u00e0-dire \\(f(x)=mx\\) alors \\(f\\) est lin\u00e9aire.<\/span><\/p>\n<p><span class=\"proprieteseconde\">Si \\(m=0\\) (c&rsquo;est-\u00e0-dire \\(f(x)=p\\) alors \\(f\\) est constante.<\/span>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text]<\/p>\n<h3>Quizz<\/h3>\n<p><div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-59\" class=\"h5p-iframe\" data-content-id=\"59\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"2nde fonction affine 1-d\u00e9finition\"><\/iframe><\/div>[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text el_id=\u00a0\u00bbobjectif-3&Prime;]<\/p>\n<h1 style=\"text-align: center;\">Repr\u00e9sentation graphique<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<span class=\"proprieteseconde\">Une fonction affine est repr\u00e9sent\u00e9e par une droite.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2774 size-full\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/representation.jpg\" alt=\"\" width=\"842\" height=\"433\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/representation.jpg 842w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/representation-300x154.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/representation-768x395.jpg 768w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/representation-806x414.jpg 806w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/representation-558x287.jpg 558w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/representation-655x337.jpg 655w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/representation-820x422.jpg 820w\" sizes=\"auto, (max-width: 842px) 100vw, 842px\" \/><\/p>\n<p><span class=\"proprieteseconde\">Les trois fonctions sont affines, la fonction \\(f\\) est en plus lin\u00e9aire, la fonction \\(g\\) est en plus constante<\/span>[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text]<\/p>\n<div style=\"text-align: center;\"><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/OnnrfqztpTY\" width=\"320\" height=\"180\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/div>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column][vc_column_text]<\/p>\n<h3>Quizz<\/h3>\n<p>On consid\u00e8re une fonction affine dans un graphique.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2784 size-full\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/quizz-2-q1.jpg\" alt=\"\" width=\"747\" height=\"431\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/quizz-2-q1.jpg 747w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/quizz-2-q1-300x173.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/quizz-2-q1-558x322.jpg 558w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/quizz-2-q1-655x378.jpg 655w\" sizes=\"auto, (max-width: 747px) 100vw, 747px\" \/><\/p>\n<p>R\u00e9pondre aux quatre questions suivantes<\/p>\n<p><div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-60\" class=\"h5p-iframe\" data-content-id=\"60\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"2nde fonction affine 2-Repr\u00e9sentation\"><\/iframe><\/div>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text el_id=\u00a0\u00bbobjectif-4&Prime;]<\/p>\n<h1 style=\"text-align: center;\">Variations et signe<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<span class=\"proprieteseconde\">Les variations d&rsquo;une fonction affine \\(x \\mapsto mx+p\\) d\u00e9pendent du signe de \\(m\\)&#8230;<\/span>[\/vc_column_text][vc_row_inner][vc_column_inner width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<\/p>\n<p style=\"text-align: center;\"><span class=\"proprieteseconde\">&#8230; croissante lorsque \\(m\\) est positif<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2780 aligncenter\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/2_fct_affines_tableau-m-positif-300x162.jpg\" alt=\"\" width=\"300\" height=\"162\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/2_fct_affines_tableau-m-positif-300x162.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/2_fct_affines_tableau-m-positif.jpg 342w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Dans ce cas, la fonction \\(f\\) est n\u00e9gative sur l&rsquo;intervalle \\(]-\\infty ; -\\frac{p}{m}[\\) et positive sur l&rsquo;intervalle \\(]-\\frac{p}{m} ; +\\infty[\\)[\/vc_column_text][\/vc_column_inner][vc_column_inner width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<\/p>\n<p style=\"text-align: center;\"><span class=\"proprieteseconde\">&#8230; d\u00e9croissante lorsque \\(m\\) est n\u00e9gatif<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2782 aligncenter\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/2_fct_affines_tableau-m-negatif-300x164.jpg\" alt=\"\" width=\"300\" height=\"164\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/2_fct_affines_tableau-m-negatif-300x164.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/02\/2_fct_affines_tableau-m-negatif.jpg 343w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Dans ce cas, la fonction \\(f\\) est positive sur l&rsquo;intervalle \\(]-\\infty ; -\\frac{p}{m}[\\) et n\u00e9gative sur l&rsquo;intervalle \\(]-\\frac{p}{m} ; +\\infty[\\)[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_row_inner][vc_column_inner][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<span class=\"proprieteseconde\">Dans tous les cas, la fonction s&rsquo;annule pour \\(x=\\displaystyle -\\frac{p}{m}\\)<\/span>[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column][vc_column_text]<\/p>\n<h3>Quizz<\/h3>\n<p>R\u00e9pondre aux questions suivantes<\/p>\n<p><div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-61\" class=\"h5p-iframe\" data-content-id=\"61\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"2nde fonction affine 3 - signe et variations\"><\/iframe><\/div>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<h2>Synth\u00e8ses :<\/h2>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_single_image source=\u00a0\u00bbexternal_link\u00a0\u00bb onclick=\u00a0\u00bbimg_link_large\u00a0\u00bb img_link_target=\u00a0\u00bb_blank\u00a0\u00bb custom_src=\u00a0\u00bbhttps:\/\/docs.google.com\/drawings\/d\/e\/2PACX-1vSxpuPuXnVV4nt7UyapI2yVQRqCkMoBjRxcgQIlfwalCUZDIIn_KPfYJ28XPg_r6UQiS3dlKjhHPWGv\/pub?w=960&amp;h=720&Prime;][vc_single_image source=\u00a0\u00bbexternal_link\u00a0\u00bb onclick=\u00a0\u00bbimg_link_large\u00a0\u00bb img_link_target=\u00a0\u00bb_blank\u00a0\u00bb custom_src=\u00a0\u00bbhttps:\/\/docs.google.com\/drawings\/d\/e\/2PACX-1vRKKO8BXkNqxt2tpXENMYX3JLBwsihopdFWohYwxV00GsL6iOxmVgU58IlkYzOr0wu7SV95obQG4piR\/pub?w=960&amp;h=720&Prime;][\/vc_column][\/vc_row]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column][vc_column_text el_id=\u00a0\u00bbobjectif-1&Prime;] D\u00e9finition [\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]Une fonction affine s&rsquo;\u00e9crit \\(f(x)=mx+p\\) \\(m\\) s&rsquo;appelle le coefficient directeur. \\(p\\) s&rsquo;appelle l&rsquo;ordonn\u00e9e \u00e0 l&rsquo;origine.[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb] Taux d&rsquo;accroissement Dans le cas des fonctions affines, le taux d&rsquo;accroissement \\(\\displaystyle \\frac{f(b)-f(a)}{b-a}\\) est constant (et \u00e9gal \u00e0 \\(m\\) )[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text] [\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]Si \\(p=0\\) (c&rsquo;est-\u00e0-dire \\(f(x)=mx\\) alors [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2085,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"folder":[],"class_list":["post-2771","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2771","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/comments?post=2771"}],"version-history":[{"count":15,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2771\/revisions"}],"predecessor-version":[{"id":3371,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2771\/revisions\/3371"}],"up":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2085"}],"wp:attachment":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/media?parent=2771"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/folder?post=2771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}