{"id":13,"date":"2023-09-17T11:11:42","date_gmt":"2023-09-17T11:11:42","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e3%83%a2%e3%83%8e%e3%83%bc%e3%83%a0%e3%81%ae%e5%88%86%e5%89%b2-%e5%88%86%e5%89%b2%e3%81%ae%e4%be%8b%e3%81%a8%e6%bc%94%e7%bf%92%e3%82%92%e8%a7%a3%e6%b1%ba%e3%81%97%e3%81%be%e3%81%97%e3%81%9f-1\/"},"modified":"2023-09-17T11:11:42","modified_gmt":"2023-09-17T11:11:42","slug":"%e3%83%a2%e3%83%8e%e3%83%bc%e3%83%a0%e3%81%ae%e5%88%86%e5%89%b2-%e5%88%86%e5%89%b2%e3%81%ae%e4%be%8b%e3%81%a8%e6%bc%94%e7%bf%92%e3%82%92%e8%a7%a3%e6%b1%ba%e3%81%97%e3%81%be%e3%81%97%e3%81%9f-1","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e3%83%a2%e3%83%8e%e3%83%bc%e3%83%a0%e3%81%ae%e5%88%86%e5%89%b2-%e5%88%86%e5%89%b2%e3%81%ae%e4%be%8b%e3%81%a8%e6%bc%94%e7%bf%92%e3%82%92%e8%a7%a3%e6%b1%ba%e3%81%97%e3%81%be%e3%81%97%e3%81%9f-1\/","title":{"rendered":"\u95a2\u6570\u5909\u63db: 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id=\"%c2%bfque-son-las-transformaciones-de-funciones\"><\/span>\u95a2\u6570\u5909\u63db\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u3059\u3067\u306b\u77e5\u3063\u3066\u3044\u308b\u4ed6\u306e\u521d\u7b49\u95a2\u6570\u3068\u3088\u304f\u4f3c\u305f\u521d\u7b49\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u5316\u3059\u308b\u3088\u3046\u306b\u6c42\u3081\u3089\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u540c\u69d8\u306e\u95a2\u6570\u3092\u518d\u5ea6\u8868\u73fe\u3059\u308b\u4ee3\u308f\u308a\u306b\u3001\u30c6\u30af\u30cb\u30c3\u30af\u3092\u4f7f\u7528\u3057\u3066\u3001\u3042\u308b\u95a2\u6570\u306e\u8868\u73fe\u304b\u3089\u5225\u306e\u95a2\u6570\u306e\u8868\u73fe\u306b\u7c21\u5358\u304b\u3064\u8fc5\u901f\u306b\u5207\u308a\u66ff\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u95a2\u6570\u5909\u63db\u306f\u3001<\/strong>\u57fa\u672c\u7684\u306a\u64cd\u4f5c\u3092\u901a\u3058\u3066\u3001\u3042\u308b\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u8868\u73fe\u304b\u3089\u5225\u306e\u975e\u5e38\u306b\u3088\u304f\u4f3c\u305f\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u8868\u73fe\u3078\u306e\u79fb\u884c\u3092\u53ef\u80fd\u306b\u3059\u308b\u6280\u8853\u3067\u3059\u3002<\/p>\n<p>\u57fa\u672c\u7684\u306b\u3001\u521d\u7b49\u95a2\u6570\u306e\u5909\u63db\u306b\u306f 3 \u3064\u306e\u30bf\u30a4\u30d7\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li><strong>\u5e73\u884c\u79fb\u52d5\u307e\u305f\u306f\u79fb\u52d5<\/strong>: \u95a2\u6570\u306f\u5782\u76f4\u65b9\u5411\u3068\u6c34\u5e73\u65b9\u5411\u306b\u79fb\u52d5\u3067\u304d\u307e\u3059\u3002<\/li>\n<li><strong>\u53cd\u6620\u307e\u305f\u306f\u5bfe\u79f0<\/strong>: X \u8ef8\u307e\u305f\u306f Y \u8ef8\u3092\u5bfe\u79f0\u8ef8\u3068\u3057\u3066\u4f7f\u7528\u3057\u3066\u3001\u95a2\u6570\u3092\u53cd\u6620\u3067\u304d\u307e\u3059\u3002<\/li>\n<li><strong>\u62e1\u5927\u30fb\u7e2e\u5c0f<\/strong>: \u95a2\u6570\u3092\u62e1\u5927\u30fb\u7e2e\u5c0f\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ul>\n<p>\u95a2\u6570\u306e\u5909\u63db\u306e\u6982\u5ff5\u3092\u7406\u89e3\u3057\u305f\u3089\u3001\u305d\u308c\u305e\u308c\u306e\u7a2e\u985e\u306e\u5909\u66f4\u3092\u3055\u3089\u306b\u8a73\u3057\u304f\u898b\u3066\u3044\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"traslaciones-o-desplazamientos-de-funciones\"><\/span>\u95a2\u6570\u306e\u5909\u63db\u307e\u305f\u306f\u79fb\u52d5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u307e\u305a\u306f\u6a5f\u80fd\u306e\u30b7\u30d5\u30c8\u304b\u3089\u59cb\u3081\u307e\u3059\u3002\u7e26\u65b9\u5411\u306e\u7ffb\u8a33\u3068\u6a2a\u65b9\u5411\u306e\u7ffb\u8a33\u306e 2 \u7a2e\u985e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\u307e\u305f\u306f\u5782\u76f4\u79fb\u52d5<\/h3>\n<p>\u95a2\u6570\u3092\u5782\u76f4\u65b9\u5411 (Y \u8ef8\u306b\u6cbf\u3063\u3066) \u306b\u5e73\u884c\u79fb\u52d5\u307e\u305f\u306f\u79fb\u52d5\u3059\u308b\u306b\u306f\u3001\u95a2\u6570\u306b\u5b9a\u6570\u3092\u52a0\u7b97\u307e\u305f\u306f\u6e1b\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<div style=\"padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\">\u95a2\u6570\u306b ka \u3092\u8ffd\u52a0\u3059\u308b\u3053\u3068\u3067\u3001\u95a2\u6570\u3092<strong>k \u5358\u4f4d\u4e0a\u306b<\/strong>\u79fb\u52d5\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d148ee17ffaab58b502ee771b74a931a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(x)+k}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u95a2\u6570\u304b\u3089 ka \u3092\u6e1b\u7b97\u3057\u3066\u3001\u95a2\u6570<strong>\u3092 k \u5358\u4f4d\u4e0b\u306b<\/strong>\u30b7\u30d5\u30c8\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76021d6fef316019d46a849b31cb7ff5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(x)-k}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/translation-ou-deplacement-vertical-d-une-fonction.webp\" alt=\"\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\u307e\u305f\u306f\u5782\u76f4\u79fb\u52d5\" class=\"wp-image-314\" width=\"401\" height=\"334\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u30b0\u30e9\u30d5\u304b\u3089\u308f\u304b\u308b\u3088\u3046\u306b\u3001\u95a2\u6570\u306b\u5b9a\u6570\u3092\u8ffd\u52a0\u3059\u308b\u3068\u3001\u8ffd\u52a0\u3055\u308c\u308b\u5358\u4f4d\u304c\u4e0a\u306b\u30b7\u30d5\u30c8\u3057\u307e\u3059 (\u7dd1\u8272\u306e\u95a2\u6570)\u3002\u4e00\u65b9\u3001\u95a2\u6570\u304b\u3089\u6570\u5024\u3092\u6e1b\u7b97\u3059\u308b\u3068\u3001\u6e1b\u7b97\u3055\u308c\u305f\u5358\u4f4d\u304c\u4e0b\u306b\u79fb\u52d5\u3057\u307e\u3059 (\u8d64\u8272\u306e\u95a2\u6570)\u3002<\/p>\n<p>\u3053\u306e\u30bf\u30a4\u30d7\u306e\u79fb\u52d5\u3067\u306f\u3001\u30d5\u30a1\u30f3\u30af\u30b7\u30e7\u30f3 \u30dd\u30a4\u30f3\u30c8\u306e Y \u5ea7\u6a19\u306e\u307f\u304c\u5909\u66f4\u3055\u308c\u3001X \u5ea7\u6a19\u306f\u540c\u3058\u307e\u307e\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\u307e\u305f\u306f\u6c34\u5e73\u79fb\u52d5<\/h3>\n<p>\u95a2\u6570\u3092\u6c34\u5e73\u65b9\u5411 (X \u8ef8\u306b\u6cbf\u3063\u3066) \u306b\u79fb\u52d5\u307e\u305f\u306f\u30b7\u30d5\u30c8\u3059\u308b\u306b\u306f\u3001\u72ec\u7acb\u5909\u6570<em>x<\/em>\u306b\u5b9a\u6570\u3092\u52a0\u7b97\u307e\u305f\u306f\u6e1b\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<div style=\"padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\">\u306e\u30b0\u30e9\u30d5<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-682fb180cfa4be390cf2d7735ddeb017_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(x+k)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u306e\u30b0\u30e9\u30d5\u3067\u3059<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p><strong>k\u5358\u4f4d\u3092\u5de6\u306b\u79fb\u52d5\u3057\u307e\u3057\u305f\u3002<\/strong><\/p>\n<p style=\"text-align:left\">\u306e\u30b0\u30e9\u30d5<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7433764880a8f4ab8e11e3f162743b49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(x-k)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u306e\u30b0\u30e9\u30d5\u3067\u3059<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p><strong>k\u5358\u4f4d\u3092\u53f3\u306b\u30b7\u30d5\u30c8\u3057\u307e\u3057\u305f\u3002<\/strong> <\/p>\n<\/div>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/translation-ou-deplacement-horizontal-d-une-fonction.webp\" alt=\"\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\u307e\u305f\u306f\u6c34\u5e73\u79fb\u52d5\" class=\"wp-image-315\" width=\"504\" height=\"323\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u30b0\u30e9\u30d5\u304b\u3089\u308f\u304b\u308b\u3088\u3046\u306b\u3001\u5b9a\u6570\u3092\u5909\u6570<em>x<\/em>\u306b\u76f4\u63a5\u8ffd\u52a0\u3059\u308b\u3068\u3001\u95a2\u6570\u306f\u8ffd\u52a0\u3055\u308c\u305f\u5358\u4f4d\u3092\u5de6\u306b\u30b7\u30d5\u30c8\u3057\u307e\u3059 (\u8d64\u3044\u95a2\u6570)\u3002\u4e00\u65b9\u3001\u5909\u6570<em>x<\/em>\u304b\u3089\u6570\u5024\u3092\u6e1b\u7b97\u3059\u308b\u5834\u5408\u3001\u95a2\u6570\u306f\u6e1b\u7b97\u3055\u308c\u305f\u5358\u4f4d\u3092\u53f3\u306b\u30b7\u30d5\u30c8\u3057\u307e\u3059 (\u7dd1\u8272\u306e\u95a2\u6570)\u3002<\/p>\n<p>\u3053\u306e\u30bf\u30a4\u30d7\u306e\u79fb\u52d5\u3067\u306f\u3001\u30d5\u30a1\u30f3\u30af\u30b7\u30e7\u30f3 \u30dd\u30a4\u30f3\u30c8\u306e X \u5ea7\u6a19\u306e\u307f\u304c\u5909\u66f4\u3055\u308c\u3001Y \u5ea7\u6a19\u306f\u540c\u3058\u5024\u3092\u7dad\u6301\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u95a2\u6570\u306e\u5909\u63db\u307e\u305f\u306f\u79fb\u52d5\u306e\u4f8b<\/h3>\n<ul>\n<li>\u6b21\u306e\u95a2\u6570\u3092\u4e0a\u306b 4 \u5358\u4f4d\u3001\u53f3\u306b 3 \u5358\u4f4d\u79fb\u52d5\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c3421a45cc1c0ad35b18520e81ddc031_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u95a2\u6570\u3092 4 \u5358\u4f4d\u4e0a\u306b\u79fb\u52d5\u3059\u308b\u306b\u306f\u3001\u95a2\u6570\u306b 4 \u5358\u4f4d\u3092\u8ffd\u52a0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42f15821de4342f9ad62ca1f3d430a5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) + 4 = x^2 + 4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u307e\u305f\u3001\u95a2\u6570\u3092\u53f3\u306b 3 \u5358\u4f4d\u79fb\u52d5\u3059\u308b\u306b\u306f\u3001\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f7b64f7ef5acc0208ecdcbf36a93b216_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"64\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u3002\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6211\u3005\u306f\u3067\u304d\u308b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bde661e1b7bc62c4e804705b7a355ef5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-3 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33a30fbf704532ac9887adb3449914a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x-3) = (x-3)^2 + 4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"181\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u4e0a\u306b 4 \u5358\u4f4d\u3001\u53f3\u306b 3 \u5358\u4f4d\u30b7\u30d5\u30c8\u3057\u305f\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d2f913b24aecd43b30aca4a2ed58e0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(x) = (x-3)^2 + 4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"151\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4ee5\u4e0b\u306b\u3001\u5143\u306e\u95a2\u6570\u3068\u5909\u63db\u3055\u308c\u305f\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u5316\u3057\u3066\u3001\u305d\u308c\u3089\u306e\u9055\u3044\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-translation-ou-deplacement-d-une-fonction.webp\" alt=\"\u95a2\u6570\u306e\u5909\u63db\u307e\u305f\u306f\u79fb\u52d5\u306e\u4f8b\" class=\"wp-image-316\" width=\"475\" height=\"374\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u6570\u5b66\u8005\u306b\u3088\u3063\u3066\u306f\u3001\u4e21\u65b9\u306e\u30bf\u30a4\u30d7\u306e\u52d5\u304d\u304c\u540c\u6642\u306b\u767a\u751f\u3059\u308b\u5834\u5408\u3001\u659c\u3081\u306e\u5909\u4f4d\u307e\u305f\u306f\u5e73\u884c\u79fb\u52d5\u3068\u547c\u3073\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"reflexion-o-simetria-de-una-funcion-respecto-los-ejes-de-coordenadas\"><\/span>\u5ea7\u6a19\u8ef8\u306b\u5bfe\u3059\u308b\u95a2\u6570\u306e\u93e1\u6620\u307e\u305f\u306f\u5bfe\u79f0\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306e\u65b9\u6cd5\u3067\u3001\u4efb\u610f\u306e\u30c7\u30ab\u30eb\u30c8\u8ef8\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u95a2\u6570\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<div style=\"padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> <strong>X \u8ef8\u306b\u95a2\u3057\u3066\u95a2\u6570\u3092\u53cd\u6620\u3059\u308b\u306b\u306f\u3001<\/strong>\u95a2\u6570\u306e\u7b26\u53f7\u3092\u5909\u66f4\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8122cbaf79d8273fae34a9c722301ef7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-f(x)}.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> <strong>y \u8ef8\u306b\u95a2\u3057\u3066\u95a2\u6570\u3092\u53cd\u6620\u3059\u308b\u306b\u306f\u3001<\/strong>\u72ec\u7acb\u5909\u6570<em>x<\/em>\u3092\u5426\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u6b21\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4367428d9a78be3de312b14e5205e6e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(-x)}.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/division-de-monomes-1.png\" alt=\"X \u8ef8\u306b\u5bfe\u3059\u308b\u53cd\u5c04\u307e\u305f\u306f\u5bfe\u79f0\" class=\"wp-image-317\" width=\"378\" height=\"312\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u524d\u306e\u30b0\u30e9\u30d5\u3067\u308f\u304b\u308b\u3088\u3046\u306b\u3001\u95a2\u6570\u306b -1 \u3092\u4e57\u7b97\u3059\u308b\u3053\u3068\u3067\u3001\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u30a3\u30ab\u30eb\u306b\u53cd\u8ee2\u3057\u307e\u3059 (\u30aa\u30ec\u30f3\u30b8\u8272\u306e\u95a2\u6570)\u3001\u8a00\u3044\u63db\u3048\u308c\u3070\u3001X \u8ef8\u306b\u5bfe\u3057\u3066\u30df\u30e9\u30fc\u30ea\u30f3\u30b0\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/reflexion-ou-symetrie-autour-de-laxe-y.webp\" alt=\"Y \u8ef8\u3092\u4e2d\u5fc3\u3068\u3057\u305f\u53cd\u5c04\u307e\u305f\u306f\u5bfe\u79f0\" class=\"wp-image-318\" width=\"378\" height=\"311\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u524d\u306e\u30b0\u30e9\u30d5\u3067\u308f\u304b\u308b\u3088\u3046\u306b\u3001\u5909\u6570<em>x<\/em>\u3092\u5426\u5b9a\u3059\u308b\u3053\u3068\u3067\u3001Y \u8ef8\u306b\u95a2\u3057\u3066\u95a2\u6570\u3092\u30df\u30e9\u30fc\u30ea\u30f3\u30b0\u3057\u307e\u3059 (\u8584\u7dd1\u8272\u306e\u95a2\u6570)\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u95a2\u6570\u306e\u30df\u30e9\u30fc\u30ea\u30f3\u30b0\u306e\u4f8b<\/h3>\n<ul>\n<li>\u6b21\u306e\u4e8c\u6b21\u95a2\u6570\u306e OX \u8ef8\u3092\u4e2d\u5fc3\u3068\u3057\u305f\u5bfe\u79f0\u95a2\u6570\u3068 OY \u8ef8\u3092\u4e2d\u5fc3\u3068\u3057\u305f\u5bfe\u79f0\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-11c8e8e3276a66729e9719a4398fac1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2-4x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"147\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> X \u8ef8\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u306a\u95a2\u6570\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d240a12433577722a9f830dc1dcf0429_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -5px;\"><\/p>\n<p> :<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ec1ca457c73589ee30ad6641f0d66c10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-f(x)=-\\bigl[x^2-4x+6\\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"185\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6cffd86481d9546a5ce3132cebe8c0d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-f(x)=-x^2+4x-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"174\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u3001Y \u8ef8\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u306a\u95a2\u6570\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u6b21\u306e\u3053\u3068\u3092\u884c\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3831e7dbe8df4202b0780cbbb20432a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"48\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3042\u308b\u5834\u6240\u3092\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5143\u306e\u95a2\u6570\u3067\u306f\u9805\u306b\u3088\u3063\u3066<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9371f1e5d1cef68566c73bc482dfa55c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"32\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-11c8e8e3276a66729e9719a4398fac1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2-4x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"147\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6481e91f5c0f1de72c88438cb4aefbce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-x)=(-x)^2-4\\cdot (-x)+6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"229\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-04737d1dbc867b60d68e9c8f38387dc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-x)=x^2-4\\cdot (-x)+6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"201\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9bb0ac917663f86bcba5cacc5d3f482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(-x)=x^2+4x+6}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"161\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4ee5\u4e0b\u306b\u3001\u5143\u306e\u95a2\u6570\u3068\u898b\u3064\u304b\u3063\u305f\u5bfe\u79f0\u95a2\u6570\u306e\u4e21\u65b9\u3092\u8868\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-fonctions-symetriques-avec-les-axes-x-et-y.webp\" alt=\"x \u8ef8\u3068 y \u8ef8\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u306a\u95a2\u6570\u306e\u4f8b\" class=\"wp-image-319\" width=\"588\" height=\"557\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"expansiones-y-contracciones-de-las-funciones\"><\/span>\u95a2\u6570\u306e\u62e1\u5f35\u3068\u7e2e\u5c0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ffb\u8a33\u3068\u540c\u69d8\u306b\u3001\u62e1\u5927\u307e\u305f\u306f\u7e2e\u5c0f\u306b\u306f\u5782\u76f4\u65b9\u5411\u3068\u6c34\u5e73\u65b9\u5411\u306e 2 \u3064\u306e\u30bf\u30a4\u30d7\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u95a2\u6570\u306e\u5782\u76f4\u65b9\u5411\u306e\u4f38\u7e2e<\/h3>\n<p>\u6574\u6570\u95a2\u6570\u306b\u4fc2\u6570\u3092\u4e57\u7b97\u3059\u308b\u3068\u3001\u95a2\u6570\u3092\u62e1\u5927\u307e\u305f\u306f\u7e2e\u5c0f\u3067\u304d\u307e\u3059\u3002 <\/p>\n<div style=\"padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> <strong>Y \u8ef8\u4e0a\u306e\u95a2\u6570\u3092\u62e1\u5927 (\u307e\u305f\u306f\u62e1\u5f35) \u3059\u308b\u306b\u306f\u3001<\/strong>\u95a2\u6570\u306b 1 \u3088\u308a\u5927\u304d\u3044\u6570\u5024\u3092\u4e57\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-03a53c8010e3a92a216e3db2ceec41fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"kf(x)\\qquad k>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;121&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p style=\"text-align:left\"> <strong>Y \u8ef8\u4e0a\u306e\u95a2\u6570\u3092\u7e2e\u5c0f\u3059\u308b\u306b\u306f\u3001<\/strong>\u95a2\u6570\u306b 1 \u672a\u6e80\u306e\u6b63\u306e\u6570\u3092\u639b\u3051\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-189e80beb9f93693ae854541fe86e22b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"kf(x)\\qquad 0<\/div>\n<div class=&quot;wp-block-image&quot;>\n<figure class=&quot;aligncenter size-large is-resized&quot;><img decoding=&quot;async&quot; loading=&quot;lazy&quot; src=&quot;http:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/expansion-et-contraction-d-une-fonction.webp&quot; alt=&quot;expansion et contraction verticales d'une fonction&quot; class=&quot;wp-image-320&quot; width=&quot;442&quot; height=&quot;438&quot; srcset=&quot;&quot; sizes=&quot;&quot; data-src=&quot;&quot;><\/figure>\n<\/div>\n<p> Comme vous pouvez le voir dans le graphique pr\u00e9c\u00e9dent, si on multiplie une fonction par un coefficient sup\u00e9rieur \u00e0 1 (fonction verte) on la rend plus grande le long de l&#8217;axe OY, en revanche, si on multiplie une fonction par un coefficient sup\u00e9rieur \u00e0 0 mais plus petit que 1 (fonction rouge), nous le rendons plus petit le long de l&#8217;axe OY.<\/p>\n<h3 class=&quot;wp-block-heading&quot;> Expansion et contraction horizontales d&#8217;une fonction<\/h3>\n<p> Dans ce cas, au lieu de multiplier la fonction enti\u00e8re par un coefficient, pour qu&#8217;une fonction se dilate ou se contracte horizontalement, nous devons multiplier la variable ind\u00e9pendante <em>x<\/em> . <\/p>\n<div style=&quot;padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;&quot;> Pour <strong>\u00e9tendre (ou dilater) une fonction sur l&#8217;axe X,<\/strong> il faut multiplier tous les <em>x<\/em> par un nombre compris entre 0 et 1 :&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;392&#8243; width=&#8221;2425&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<p> f(kx)\\qquad 0<\/p>\n<p style=\"text-align:left\"> <strong>X \u8ef8\u4e0a\u306e\u95a2\u6570\u3092\u7e2e\u5c0f\u3059\u308b\u306b\u306f\u3001<\/strong>\u3059\u3079\u3066\u306e<em>x<\/em>\u306b 1 \u3088\u308a\u5927\u304d\u3044\u6570\u3092\u639b\u3051\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-172c2c9b2f320ce017a42e21495fc0e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(kx)\\qquad k>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;121&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/contraction-horizontale-ou-expansion-d-une-fonction.webp\" alt=\"\u95a2\u6570\u306e\u6c34\u5e73\u65b9\u5411\u306e\u62e1\u5f35\u307e\u305f\u306f\u7e2e\u5c0f\" class=\"wp-image-321\" width=\"446\" height=\"413\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u524d\u306e\u30b0\u30e9\u30d5\u3067\u308f\u304b\u308b\u3088\u3046\u306b\u3001\u95a2\u6570\u306e\u3059\u3079\u3066\u306e<em>x<\/em>\u306b 0 \u3088\u308a\u5927\u304d\u304f 1 \u672a\u6e80\u306e\u4fc2\u6570\u3092\u639b\u3051\u308b\u3068 (\u7dd1\u306e\u95a2\u6570)\u3001OX \u8ef8\u306b\u6cbf\u3063\u3066\u62e1\u5927\u3055\u308c\u307e\u3059\u3002 1 \u3088\u308a\u5927\u304d\u3044\u4fc2\u6570\u306b\u3088\u308b\u95a2\u6570 (\u8d64\u8272\u306e\u95a2\u6570) \u3092 OX \u8ef8\u306b\u6cbf\u3063\u3066\u7e2e\u5c0f\u3057\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u95a2\u6570\u3092\u5c55\u958b\u307e\u305f\u306f\u6298\u308a\u305f\u305f\u3080\u65b9\u6cd5\u306e\u4f8b<\/h3>\n<ul>\n<li>\u6b21\u306e\u7121\u7406\u95a2\u6570\u3092\u5782\u76f4\u65b9\u5411\u3068\u6c34\u5e73\u65b9\u5411\u306b\u8907\u88fd\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df182b1121b5047a370b9a0217f223b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{9-x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"122\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> y \u8ef8\u4e0a\u306e\u95a2\u6570\u3092 2 \u500d\u306b\u62e1\u5f35\u3059\u308b\u306b\u306f\u3001\u95a2\u6570\u5168\u4f53\u3092 2 \u500d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f10c9a73b34546e1fb103b07d188c16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2f(x)=2\\sqrt{9-x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"140\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u307e\u305f\u3001\u95a2\u6570\u3092 x \u8ef8\u3067 2 \u500d\u306b\u62e1\u5f35\u3059\u308b\u306b\u306f\u3001\u95a2\u6570\u306e\u3059\u3079\u3066\u306e<em>x<\/em>\u306b\u6b21\u306e\u5024\u3092\u4e57\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cc880ad231c4b13f10b0a4b05da2aed9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{1}{2}:\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"20\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7955c308d702a9df6603dde57400f31d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f\\left(\\frac{1}{2}x\\right)=2\\sqrt{9-\\left(\\frac{1}{2}x\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"201\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u5ea7\u6a19\u8ef8\u4e0a\u3067\u8907\u88fd\u3055\u308c\u308b\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-891161dec71142b1dc7c87250a039b6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\bm{f(x) = 2\\sqrt{9-\\left(\\frac{1}{2}x\\right)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"173\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p>\u4ee5\u4e0b\u306b\u3001\u5143\u306e\u95a2\u6570\u3068\u5909\u63db\u3055\u308c\u305f\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u3067\u793a\u3057\u3001\u305d\u308c\u3089\u306e\u9055\u3044\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-comment-developper-et-reduire-une-fonction.webp\" alt=\"\u95a2\u6570\u3092\u5c55\u958b\u304a\u3088\u3073\u6298\u308a\u305f\u305f\u3080\u65b9\u6cd5\u306e\u4f8b\" class=\"wp-image-322\" width=\"434\" height=\"395\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u65b0\u3057\u3044\u30d5\u30a3\u30fc\u30c1\u30e3 (\u7d2b\u8272) \u306f\u5143\u306e\u30d5\u30a3\u30fc\u30c1\u30e3 (\u9752\u8272) \u306e\u7e26\u65b9\u5411\u3068\u6a2a\u65b9\u5411\u306e\u4e21\u65b9\u3067 2 \u500d\u306e\u5927\u304d\u3055\u306b\u306a\u3063\u3066\u304a\u308a\u3001\u30d5\u30a3\u30fc\u30c1\u30e3\u304c\u62e1\u5f35\u3055\u308c\u3066\u3044\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-transformaciones-de-funciones\"><\/span>\u95a2\u6570\u5909\u63db\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1<\/h3>\n<p>\u6b21\u306e 3 \u6b21\u95a2\u6570\u3092 5 \u5358\u4f4d\u4e0a\u306b\u79fb\u52d5\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-40118044e198dd521201b4934a2465d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = 4x^3-9x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"155\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u95a2\u6570\u3092 5 \u5358\u4f4d\u4e0a\u306b\u79fb\u52d5\u3059\u308b\u306b\u306f\u3001\u95a2\u6570\u306b 5 \u3092\u8ffd\u52a0\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d29d1537293d975f7fbda8871622660f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} f(x) + 5 &amp; = 4x^3-9x-2 + 5 \\\\[2ex] &amp; = 4x^3-9x+3 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"216\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u30015 \u5358\u4f4d\u30b7\u30d5\u30c8\u3055\u308c\u305f\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0d7c13d80c2d91f99f6a960223c4b904_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(x) = 4x^3-9x+3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 2<\/h3>\n<p>\u6b21\u306e\u4e8c\u6b21\u95a2\u6570\u306e Y \u8ef8\u3092\u4e2d\u5fc3\u3068\u3057\u305f\u5bfe\u79f0\u95a2\u6570\u3092\u6c42\u3081\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b91b7f45206484f6878a73f6891805a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = 2x^2-3x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">Y \u8ef8\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u306a\u95a2\u6570\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u6b21\u306e\u8a08\u7b97\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3831e7dbe8df4202b0780cbbb20432a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"48\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u3064\u307e\u308a\u3001\u7f6e\u304d\u63db\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u306e\u305f\u3081\u306b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6cacb15a7aa187378723791e7a017ae0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"23\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u95a2\u6570\u5185: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-89980b1b6f9a88ffbf9ad6330aa357e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-x) = 2(-x)^2-3\\cdot (-x)+6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"238\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-488db09618c47a0ad47b0d2e5d9a219d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-x) = 2x^2+3x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"170\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001OY \u8ef8\u306b\u95a2\u3059\u308b\u5bfe\u79f0\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1ea68e782a0f7a69044cf73162fa23c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(x) = 2x^2+3x+6}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 3<\/h3>\n<p>\u6b21\u306e\u95a2\u6570\u306e\u6c34\u5e73\u5727\u7e2e\u3092\u305d\u306e\u8868\u73fe\u306e 3 \u5206\u306e 1 \u306b\u5b9f\u884c\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-312a893921ce7ac95eb3d5a4ede6fbeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = x^3-4x^2-5x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"195\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"><em>\u6a5f\u80fd<\/em><em>\u3092<\/em>\u524a\u6e1b\u3059\u308b\u306b\u306f\u3001 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32f949a88dd584d81674904f2acc7bbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3x) = (3x)^3-4(3x)^2-5(3x)+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"271\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bdb33583bf5172f677c39cee38e5b22a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3x) = 27x^3-4\\cdot 9 x^2-15x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"252\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad5277a59fdcd9e0200b2a0e20f2a8ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3x) = 27x^3-36 x^2-15x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"239\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u7e2e\u5c0f\u3055\u308c\u305f\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd28fc9dab2beff532a89bd1e056c649_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(x) = 27x^3-36 x^2-15x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"230\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 4<\/h3>\n<p> 4 \u5358\u4f4d\u53f3\u306b\u5909\u63db\u3055\u308c\u305f\u6b21\u306e\u95a2\u6570\u306e OX \u8ef8\u306b\u95a2\u3059\u308b\u5bfe\u79f0\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fb19b7a548b34b8dc54dec33a00d890e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = 3x^3-x^2+5x+8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"196\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5bfe\u79f0\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u524d\u306b\u3001\u307e\u305a\u95a2\u6570\u3092\u53f3\u306b 4 \u5358\u4f4d\u79fb\u52d5\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce682e35d129267d2d363e05fd32a40e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x-4) = 3(x-4)^3-(x-4)^2+5(x-4)+8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"359\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5f9fc4ca8d47f94f0168180fc84c65c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x-4) = 3(x-4)^3-(x-4)^2+5x-20+8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"354\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26f080aa9528ce8b84e4f3d86cea6863_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x-4) = 3(x-4)^3-(x-4)^2+5x-12\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"323\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u95a2\u6570\u3092\u79fb\u52d5\u3057\u305f\u3089\u3001X \u8ef8\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u306a\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u53d6\u5f97\u3057\u305f\u95a2\u6570\u3092\u5426\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-62a7ea0e19503ec030dcdaa59c9157eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -f(x) = -\\Bigl[3(x-4)^3-(x-4)^2+5x-12\\Bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"333\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-45bad0a6a17349b172cede9f5e0bddd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-f(x) = -3(x-4)^3+(x-4)^2-5x+12\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"319\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3064\u307e\u308a\u3001\u3059\u3079\u3066\u306e\u57fa\u672c\u64cd\u4f5c\u3092\u9069\u7528\u3057\u305f\u5f8c\u306e\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b7f02414a5ebdaa48088284628d47e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(x) =-3(x-4)^3+(x-4)^2-5x+12}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"306\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 5<\/h3>\n<p>\u6b21\u306e\u95a2\u6570\u3092\u5de6\u306b 2 \u5358\u4f4d\u30b7\u30d5\u30c8\u3057\u3066\u304b\u3089\u3001\u5782\u76f4\u65b9\u5411\u306b 4 \u500d\u306b\u62e1\u5f35\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3c33aacf88564e0d25f513ad302b229f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = x^4-5x^3-x-3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"187\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u307e\u305a\u3001\u95a2\u6570\u3092 2 \u5358\u4f4d\u5de6\u306b\u79fb\u52d5\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-126c5a402b4694c6f828f8afff050bb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x+2) = (x+2)^4-5(x+2)^3-(x+2)-3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"350\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fbde42766323610c75cf99f1fa119f16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x-4) = (x+2)^4-5(x+2)^3-x-2-3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"336\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c6805820552c93988723905b4a0ae4f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x-4) = (x+2)^4-5(x+2)^3-x-5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"305\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b21\u306b\u3001\u4fc2\u6570 4 \u3092\u4f7f\u7528\u3057\u3066\u95a2\u6570\u3092 Y \u8ef8\u306b\u6cbf\u3063\u3066\u5c55\u958b\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-07175c64db9d7e8074852df8944df6c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot f(x) = 4\\cdot \\Bigl[(x+2)^4-5(x+2)^3-x-5\\Bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"332\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-580d477d32f0bfe0890bf4300ea6d7e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = 4(x+2)^4-20(x+2)^3-4x-20\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"311\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7d50\u8ad6\u3068\u3057\u3066\u3001\u3059\u3079\u3066\u306e\u57fa\u672c\u5909\u63db\u3092\u9069\u7528\u3057\u305f\u5f8c\u306e\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1109677d4c80d5ddd4796c61d491ec43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f(x) =4(x+2)^4-20(x+2)^3-4x-20}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"311\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 6<\/h3>\n<p>\u95a2\u6570\u304b\u3089<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dad1214b336820b0d687af311863cb5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x,\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u30b0\u30e9\u30d5\u4e0a\u306e\u3069\u306e\u8868\u73fe\u304c\u95a2\u6570\u306b\u5bfe\u5fdc\u3059\u308b\u304b\u3092\u6c7a\u5b9a\u3059\u308b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-89346440ae4c39502126b23a77a33d48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x-3 .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-resolus-de-transformations-de-fonctions.webp\" alt=\"\u95a2\u6570\u5909\u63db\u306b\u3064\u3044\u3066\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3055\u308c\u308b\u6f14\u7fd2\" class=\"wp-image-323\" width=\"345\" height=\"452\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u95a2\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7dd7ee1df01702798c0545a0e677dd7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x-3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u95a2\u6570\u3067\u3059<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-983fed5b7a164bfcb0d3e0b5cebfd4c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"68\" style=\"vertical-align: -5px;\"><\/p>\n<p>3\u30e6\u30cb\u30c3\u30c8\u4e0b\u306b\u79fb\u52d5\u3057\u307e\u3057\u305f\u3002\u95a2\u6570\u304b\u3089\u6570\u5024\u3092\u5f15\u304f\u3068\u3001\u95a2\u6570\u304c\u4e0b\u306b\u79fb\u52d5\u3059\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u8868\u73fe\u306f\u3001<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7dd7ee1df01702798c0545a0e677dd7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x-3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -5px;\"><\/p>\n<p><strong>\u7dda b)<\/strong>\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u7dda\u3068\u6bd4\u8f03\u3057\u3066 3 \u5358\u4f4d\u4e0b\u306b\u30b7\u30d5\u30c8\u3057\u3066\u3044\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b66617657d81f989c6c5d4683e180df7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3053\u308c\u306f\u7e26\u8ef8\u3092\u898b\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-983fed5b7a164bfcb0d3e0b5cebfd4c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"68\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u304c 0 \u3092\u901a\u904e\u3059\u308b\u3068\u3001\u8d64\u3044\u7dda\u306f -3 \u3092\u901a\u904e\u3059\u308b\u305f\u3081\u30013 \u5358\u4f4d\u4e0b\u306b\u30b7\u30d5\u30c8\u3055\u308c\u307e\u3059\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 7<\/h3>\n<p>\u95a2\u6570\u304b\u3089<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e1bdc795bee6a8b1a1919130f22ed548_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+2,\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u3069\u306e\u653e\u7269\u7dda\u304c\u95a2\u6570\u3092\u8868\u73fe\u3057\u3066\u3044\u308b\u304b\u3092\u6c7a\u5b9a\u3059\u308b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-805285c257f852940155a59881e77197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(x-6)^2+2 .\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"155\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/problemes-resolus-de-transformations-de-fonctions.webp\" alt=\"\u95a2\u6570\u5909\u63db\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f\" class=\"wp-image-324\" width=\"586\" height=\"350\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u95a2\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34a59683b5fe280b2ad03b3a77d12552_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(x-6)^2+2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"150\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u95a2\u6570\u3067\u3059<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e5bac9d65f6cadab9818bc92de4830f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<p>6\u30e6\u30cb\u30c3\u30c8\u53f3\u306b\u79fb\u52d5\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u8a08\u7b97\u3057\u3066\u78ba\u8a8d\u3067\u304d\u307e\u3059<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-08c4660cf5137f59fa8264aa436dfdbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x-6):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e5bac9d65f6cadab9818bc92de4830f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7f2572ed3c877df9b660d302e833e334_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x-6)=(x-6)^2+2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"180\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u8868\u73fe\u306f\u3001<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34a59683b5fe280b2ad03b3a77d12552_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(x-6)^2+2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"150\" style=\"vertical-align: -5px;\"><\/p>\n<p><strong>\u653e\u7269\u7dda c)<\/strong>\u306b\u76f8\u5f53\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u653e\u7269\u7dda c) \u3068\u6bd4\u8f03\u3057\u3066\u53f3\u306b 6 \u5358\u4f4d\u30b7\u30d5\u30c8\u3057\u3066\u3044\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e5bac9d65f6cadab9818bc92de4830f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u3002<\/p>\n<p class=\"has-text-align-left\">\u3053\u308c\u306f\u3001\u653e\u7269\u7dda\u306e\u9802\u70b9\u3092\u898b\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u653e\u7269\u7dda\u306e\u9802\u70b9\u9593\u306e\u8ddd\u96e2\u3067\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e5bac9d65f6cadab9818bc92de4830f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u653e\u7269\u7dda c) \u306e\u9802\u70b9\u306f 6 \u5358\u4f4d\u306a\u306e\u3067\u3001\u5f8c\u8005\u306f\u6700\u521d\u306e\u3082\u306e\u3068\u6bd4\u8f03\u3057\u3066\u53f3\u306b 6 \u5358\u4f4d\u30b7\u30d5\u30c8\u3057\u307e\u3059\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u3001\u95a2\u6570\u5909\u63db\u3068\u306f\u4f55\u304b\u3001\u304a\u3088\u3073\u305d\u306e\u691c\u7d22\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u5909\u63db\u306b\u306f\u3001\u5e73\u884c\u79fb\u52d5 (\u307e\u305f\u306f\u5909\u4f4d)\u3001\u5bfe\u79f0\u3001\u304a\u3088\u3073\u62e1\u5f35 (\u307e\u305f\u306f\u53ce\u7e2e) \u306e 3 \u3064\u306e\u30bf\u30a4\u30d7\u304c\u3042\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u7591\u554f\u3092\u6b8b\u3055\u305a\u306b\u7df4\u7fd2\u3057\u3066\u6982\u5ff5\u3092\u7406\u89e3\u3067\u304d\u308b\u3088\u3046 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e3%83%a2%e3%83%8e%e3%83%bc%e3%83%a0%e3%81%ae%e5%88%86%e5%89%b2-%e5%88%86%e5%89%b2%e3%81%ae%e4%be%8b%e3%81%a8%e6%bc%94%e7%bf%92%e3%82%92%e8%a7%a3%e6%b1%ba%e3%81%97%e3%81%be%e3%81%97%e3%81%9f-1\/\"> <span class=\"screen-reader-text\">\u95a2\u6570\u5909\u63db: \u5e73\u884c\u79fb\u52d5\u3001\u5bfe\u79f0\u3001\u62e1\u5f35\u3001\u5727\u7e2e<\/span> \u3082\u3063\u3068\u8aad\u3080 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