{"id":3317,"date":"2021-02-15T08:06:15","date_gmt":"2021-02-15T07:06:15","guid":{"rendered":"http:\/\/jhmaths.fr\/?page_id=3317"},"modified":"2021-02-15T08:40:14","modified_gmt":"2021-02-15T07:40:14","slug":"fonctions-exponentielles","status":"publish","type":"page","link":"https:\/\/jhmaths.fr\/index.php\/terminale-technologique\/fonctions-exponentielles\/","title":{"rendered":"Fonctions exponentielles"},"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][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]<b>Pour un nombre \\(a\\) positif, on prolonge le principe de suite g\u00e9om\u00e9trique de raison \\(a\\) \u00e0 celui de fonction.<\/b><\/p>\n<p>On passe de la suite de raison \\(a\\) \\(u(n)=a^n\\) (pour \\(n\\) un nombre entier) \u00e0 la fonction \\((x)=a^x\\) (pour \\(x\\) un nombre r\u00e9el) appel\u00e9e <strong>fonction exponentielle de base<\/strong> \\(a\\).<\/p>\n<p>&nbsp;<\/p>\n<p>Cette fonction est d\u00e9finie sur \\(]-\\infty ; + \\infty[\\) (donc aussi pour \\(x\\) n\u00e9gatif)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3318 size-full\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/de-la-suite-geometrique-a-la-fonction-exponentielle.jpg\" alt=\"\" width=\"959\" height=\"762\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/de-la-suite-geometrique-a-la-fonction-exponentielle.jpg 959w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/de-la-suite-geometrique-a-la-fonction-exponentielle-300x238.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/de-la-suite-geometrique-a-la-fonction-exponentielle-768x610.jpg 768w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/de-la-suite-geometrique-a-la-fonction-exponentielle-806x640.jpg 806w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/de-la-suite-geometrique-a-la-fonction-exponentielle-558x443.jpg 558w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/de-la-suite-geometrique-a-la-fonction-exponentielle-655x520.jpg 655w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/de-la-suite-geometrique-a-la-fonction-exponentielle-820x652.jpg 820w\" sizes=\"auto, (max-width: 959px) 100vw, 959px\" \/>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text el_id=\u00a0\u00bbobjectif-2&Prime;]<\/p>\n<h1 style=\"text-align: center;\">Variations<\/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\u00bbproprietepremieresthr propriete\u00a0\u00bb]Si \\(a &gt; 1\\) , la fonction \\(x \\mapsto a^x\\) est croissante sur \\(\\mathbb{R}\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-3323 aligncenter\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/fct-exp-a-positif-300x231.jpg\" alt=\"\" width=\"300\" height=\"231\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/fct-exp-a-positif-300x231.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/fct-exp-a-positif-558x429.jpg 558w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/fct-exp-a-positif.jpg 650w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]Si \\(a &lt; 1\\), la fonction \\(x \\mapsto a^x\\) est d\u00e9croissante sur \\(\\mathbb{R}\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-3325 aligncenter\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/fct-exp-a-negatif-300x234.jpg\" alt=\"\" width=\"300\" height=\"234\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/fct-exp-a-negatif-300x234.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/fct-exp-a-negatif-558x436.jpg 558w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/fct-exp-a-negatif-655x511.jpg 655w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/02\/fct-exp-a-negatif.jpg 657w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>[\/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\/YQoR7CFM_1U\" 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]<\/p>\n<h3 style=\"text-align: center;\">Quizz<\/h3>\n<p style=\"text-align: center;\"><div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-81\" class=\"h5p-iframe\" data-content-id=\"81\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"TST2S - Fonctions exponentielles - Quizz\"><\/iframe><\/div><\/p>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text el_id=\u00a0\u00bbobjectif-3&Prime;]<\/p>\n<h1 style=\"text-align: center;\">Propri\u00e9t\u00e9s alg\u00e9briques<\/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\u00bbproprietepremieresthr propriete\u00a0\u00bb]Pour tout nombre \\(a\\) positif, pour tous nombres \\(x\\) et \\(y\\) r\u00e9els,<\/p>\n<ul>\n<li>\\(a^{x+y}=a^x \\times a^y\\)<\/li>\n<li>\\(a^{x-y}=\\displaystyle \\frac{a^x}{a^y}\\)<\/li>\n<li>\\(a^{nx}=\\left(a^x \\right)^n\\)<\/li>\n<\/ul>\n<p>[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<h2 style=\"text-align: center;\">Plan de travail<\/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-1vTZsxeBGbmWGusFmbsu3p7k2XT_fvPhdDh7Mat31UJU8oRF9KZXdsSVZiJdQ-Vlnowjd9XVsjhIIGlP\/pub?w=960&amp;h=720&Prime;][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<h2 style=\"text-align: center;\">Synth\u00e8se<\/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-1vRvEaYu1fD-toXyYyJg0DnoApbZoi6YbjFNyjORBcXMuZu6amQEMPqQNUBcW-i82ptNZI_5KNw1u53y\/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][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]Pour un nombre \\(a\\) positif, on prolonge le principe de suite g\u00e9om\u00e9trique de raison \\(a\\) \u00e0 celui de fonction. On passe de la suite de raison \\(a\\) \\(u(n)=a^n\\) (pour \\(n\\) un nombre entier) \u00e0 la fonction \\((x)=a^x\\) (pour \\(x\\) un nombre r\u00e9el) appel\u00e9e fonction exponentielle de base \\(a\\). &nbsp; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3063,"menu_order":4,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"folder":[],"class_list":["post-3317","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3317","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=3317"}],"version-history":[{"count":8,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3317\/revisions"}],"predecessor-version":[{"id":3329,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3317\/revisions\/3329"}],"up":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3063"}],"wp:attachment":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/media?parent=3317"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/folder?post=3317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}