{"id":13,"date":"2023-09-17T11:11:42","date_gmt":"2023-09-17T11:11:42","guid":{"rendered":"https:\/\/mathority.org\/id\/pembagian-monoma-membagi-contoh-dan-latihan-yang-diselesaikan-1\/"},"modified":"2023-09-17T11:11:42","modified_gmt":"2023-09-17T11:11:42","slug":"pembagian-monoma-membagi-contoh-dan-latihan-yang-diselesaikan-1","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/pembagian-monoma-membagi-contoh-dan-latihan-yang-diselesaikan-1\/","title":{"rendered":"Transformasi fungsi: terjemahan, simetri, ekspansi dan kompresi"},"content":{"rendered":"<p>Halaman ini menjelaskan apa itu transformasi fungsi dan cara menemukannya. Ada tiga jenis transformasi: translasi (atau perpindahan), simetri, dan ekspansi (atau kontraksi). Anda juga akan menemukan latihan diselesaikan langkah demi langkah sehingga Anda dapat berlatih dan memahami konsep tanpa meninggalkan keraguan. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-las-transformaciones-de-funciones\"><\/span> Apa yang dimaksud dengan transformasi fungsi?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Terkadang kita mungkin diminta untuk membuat grafik fungsi dasar yang sangat mirip dengan fungsi lain yang sudah kita ketahui. Nah, daripada merepresentasikan fungsi serupa lagi, teknik dapat digunakan untuk beralih dari merepresentasikan satu fungsi ke fungsi lainnya dengan mudah dan cepat.<\/p>\n<p> Jadi, <strong>transformasi fungsi<\/strong> adalah teknik yang memungkinkan perpindahan dari representasi grafis suatu fungsi ke representasi grafis dari fungsi lain yang sangat mirip melalui operasi dasar.<\/p>\n<p> Pada dasarnya ada tiga jenis transformasi fungsi dasar:<\/p>\n<ul>\n<li> <strong>Terjemahan atau pergerakan<\/strong> : suatu fungsi dapat dipindahkan secara vertikal dan horizontal.<\/li>\n<li> <strong>Pemantulan atau kesimetrian<\/strong> : Suatu fungsi dapat dicerminkan dengan menggunakan sumbu X atau sumbu Y sebagai sumbu simetrinya.<\/li>\n<li> <strong>Ekspansi dan kompresi<\/strong> : Suatu fungsi dapat diperbesar atau diperkecil.<\/li>\n<\/ul>\n<p> Setelah kita melihat konsep transformasi suatu fungsi, kita akan mempelajari lebih dalam setiap jenis modifikasinya. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"traslaciones-o-desplazamientos-de-funciones\"><\/span> Terjemahan atau perpindahan fungsi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Kita akan mulai dengan peralihan fungsi. Ada dua jenis: terjemahan vertikal dan terjemahan horizontal.<\/p>\n<h3 class=\"wp-block-heading\"> Terjemahan atau pergerakan vertikal suatu fungsi<\/h3>\n<p> Untuk menerjemahkan atau memindahkan suatu fungsi secara vertikal (sepanjang sumbu Y), Anda harus menambah atau mengurangi konstanta ke fungsi tersebut: <\/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\"> Kita menaikkan fungsi <strong>k satuan<\/strong> dengan menambahkan ka ke fungsi tersebut:<\/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\"> Kita menggeser suatu fungsi <strong>k satuan ke bawah<\/strong> dengan mengurangkan ka dari fungsi tersebut: <\/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=\"Terjemahan atau pergerakan vertikal suatu fungsi\" class=\"wp-image-314\" width=\"401\" height=\"334\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Seperti yang Anda lihat dari grafik, menambahkan konstanta ke fungsi apa pun akan menggeser unit yang ditambahkan ke atas (fungsi hijau). Sebaliknya, saat mengurangkan suatu bilangan dari suatu fungsi, satuan yang dikurangi akan dipindahkan ke bawah (fungsi merah).<\/p>\n<p> Perhatikan bahwa dalam jenis pergerakan ini hanya koordinat Y dari titik-titik fungsi yang diubah, sedangkan koordinat X tetap sama.<\/p>\n<h3 class=\"wp-block-heading\"> Terjemahan atau perpindahan fungsi secara horizontal<\/h3>\n<p> Untuk menerjemahkan atau menggeser suatu fungsi secara horizontal (sepanjang sumbu X), Anda harus menambah atau mengurangi sebuah konstanta pada variabel bebas <em>x<\/em> : <\/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\"> Grafik dari<\/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> adalah grafik dari<\/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> memindahkan <strong>k unit ke kiri.<\/strong><\/p>\n<p style=\"text-align:left\"> Grafik dari<\/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> adalah grafik dari<\/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> menggeser <strong>k satuan ke kanan.<\/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=\"Terjemahan atau pergerakan horizontal suatu fungsi\" class=\"wp-image-315\" width=\"504\" height=\"323\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Seperti yang Anda lihat dari grafik, saat menambahkan konstanta langsung ke variabel <em>x<\/em> , fungsi tersebut menggeser unit yang ditambahkan ke kiri (fungsi merah). Sebaliknya, saat mengurangkan suatu bilangan dari variabel <em>x<\/em> , fungsinya akan menggeser satuan yang dikurangi ke kanan (fungsi hijau).<\/p>\n<p> Perhatikan bahwa pada jenis pergerakan ini, hanya koordinat X dari titik fungsi yang diubah, sedangkan koordinat Y tetap dengan nilai yang sama.<\/p>\n<h3 class=\"wp-block-heading\"> Contoh menerjemahkan atau memindahkan suatu fungsi<\/h3>\n<ul>\n<li> Pindahkan fungsi berikut 4 satuan ke atas dan 3 satuan ke kanan:<\/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> Untuk menaikkan fungsi tersebut sebanyak 4 satuan, kita perlu menambahkan 4 satuan pada fungsi tersebut:<\/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> Dan untuk juga memindahkan fungsi tersebut sebanyak 3 satuan ke kanan kita harus menghitungnya<\/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> . Oleh karena itu, dimana terdapat a<\/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> kita dapat<\/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> Fungsinya bergeser 4 satuan ke atas dan 3 satuan ke kanan adalah:<\/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> Di bawah ini Anda memiliki grafik fungsi asli dan fungsi yang diubah sehingga Anda dapat melihat perbedaan di antara keduanya: <\/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=\"contoh translasi atau perpindahan suatu fungsi\" class=\"wp-image-316\" width=\"475\" height=\"374\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Beberapa ahli matematika menyebut perpindahan miring atau translasi ketika kedua jenis gerak terjadi pada waktu yang bersamaan. <\/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> Refleksi atau simetri suatu fungsi terhadap sumbu koordinat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Kita dapat merepresentasikan fungsi simetris terhadap sembarang sumbu kartesius dengan cara berikut: <\/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\"> Untuk <strong>merefleksikan suatu fungsi terhadap sumbu x,<\/strong> kita perlu mengubah tanda fungsi tersebut, yaitu kita perlu menghitung<\/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\"> Untuk <strong>merefleksikan suatu fungsi terhadap sumbu y,<\/strong> kita harus meniadakan variabel bebas <em>x<\/em> , yaitu kita harus menghitung <\/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=\"refleksi atau simetri terhadap sumbu X\" class=\"wp-image-317\" width=\"378\" height=\"312\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Seperti yang Anda lihat pada grafik sebelumnya, dengan mengalikan suatu fungsi dengan -1, kita membalikkannya secara grafis (fungsi oranye), atau dengan kata lain, kita mencerminkannya relatif terhadap sumbu X. <\/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=\"refleksi atau simetri terhadap sumbu Y\" class=\"wp-image-318\" width=\"378\" height=\"311\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Seperti dapat dilihat pada grafik sebelumnya, dengan meniadakan variabel <em>x<\/em> , kita mencerminkan fungsi tersebut terhadap sumbu Y (fungsi hijau muda).<\/p>\n<h3 class=\"wp-block-heading\"> Contoh mencerminkan suatu fungsi<\/h3>\n<ul>\n<li> Hitung fungsi simetris terhadap sumbu OX dan fungsi simetris terhadap sumbu OY dari fungsi kuadrat berikut:<\/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> Untuk mencari fungsi yang simetris terhadap sumbu X, kita harus melakukannya<\/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> Dan untuk mencari fungsi yang simetris terhadap sumbu Y harus kita lakukan<\/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> . Oleh karena itu, kami mengganti jika ada a<\/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> dalam fungsi aslinya dengan istilah tersebut <\/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> Di bawah ini Anda telah mewakili fungsi asli dan fungsi simetris yang ditemukan: <\/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=\"contoh fungsi simetris terhadap sumbu x dan y\" 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> Fungsi ekspansi dan kontraksi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Seperti halnya terjemahan, ada dua jenis perluasan atau kontraksi: vertikal dan horizontal.<\/p>\n<h3 class=\"wp-block-heading\"> Ekspansi dan kontraksi vertikal suatu fungsi<\/h3>\n<p> Dengan mengalikan fungsi bilangan bulat dengan koefisien, kita dapat membuatnya mengembang atau menyusut: <\/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\"> Untuk <strong>memperluas (atau melebarkan) suatu fungsi pada sumbu Y,<\/strong> kita perlu mengalikannya dengan angka yang lebih besar dari 1:<\/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\"> Untuk <strong>mereduksi suatu fungsi pada sumbu Y,<\/strong> kita perlu mengalikannya dengan bilangan positif yang kurang dari 1:<\/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)\\qkuad 0<\/p>\n<p style=\"text-align:left\"> Untuk <strong>mereduksi fungsi pada sumbu X,<\/strong> kita perlu mengalikan semua <em>x<\/em> dengan angka yang lebih besar dari 1: <\/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=\"ekspansi atau kontraksi horizontal suatu fungsi\" class=\"wp-image-321\" width=\"446\" height=\"413\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Seperti yang Anda lihat pada grafik sebelumnya, jika kita mengalikan semua <em>x<\/em> suatu fungsi dengan koefisien yang lebih besar dari 0 tetapi kurang dari 1 (fungsi hijau), kita memperbesarnya sepanjang sumbu OX, sebaliknya jika kita mengalikannya fungsi dengan koefisien lebih besar dari 1 (fungsi merah) kita kurangi sepanjang sumbu OX.<\/p>\n<h3 class=\"wp-block-heading\"> Contoh cara memperluas atau menciutkan suatu fungsi<\/h3>\n<ul>\n<li> Gandakan fungsi irasional berikut secara vertikal dan horizontal:<\/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> Untuk memperluas fungsi pada sumbu y dengan dua, kita harus mengalikan seluruh fungsi dengan 2:<\/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> Dan untuk memperluas fungsi tersebut dengan dua pada sumbu x, kita harus mengalikan semua <em>x<\/em> dari fungsi tersebut dengan<\/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> Oleh karena itu, fungsi yang diduplikasi pada dua sumbu koordinat adalah:<\/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> Di bawah ini Anda memiliki fungsi asli dan fungsi yang diubah direpresentasikan secara grafis sehingga Anda dapat melihat perbedaan di antara keduanya: <\/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=\"contoh cara memperluas dan menciutkan suatu fungsi\" class=\"wp-image-322\" width=\"434\" height=\"395\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Seperti yang Anda lihat, fitur baru (warna ungu) berukuran dua kali lebih besar dari fitur asli (warna biru) baik secara vertikal maupun horizontal, oleh karena itu fitur tersebut diperluas. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-transformaciones-de-funciones\"><\/span> Latihan soal transformasi fungsi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Pindahkan fungsi derajat ketiga berikut ini ke atas sebanyak 5 satuan: <\/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>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk menaikkan fungsi sebanyak 5 satuan, tambahkan 5 ke fungsi tersebut:<\/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\"> Maka fungsi yang digeser sebanyak 5 satuan adalah: <\/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\">Latihan 2<\/h3>\n<p> Temukan fungsi simetris terhadap sumbu Y dari fungsi kuadrat berikut: <\/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>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mencari fungsi yang simetris terhadap sumbu Y perlu dilakukan perhitungan<\/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> , artinya, kita perlu menggantinya<\/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> Untuk<\/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> dalam fungsi: <\/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\"> Oleh karena itu, fungsi simetris terhadap sumbu OY adalah: <\/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\">Latihan 3<\/h3>\n<p> Lakukan kompresi horizontal fungsi berikut hingga sepertiga representasinya: <\/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>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mengurangi <em>suatu<\/em> <em>fungsi<\/em> melalui <\/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\"> Oleh karena itu, fungsi tereduksinya adalah: <\/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\">Latihan 4<\/h3>\n<p> Hitung fungsi simetris terhadap sumbu OX dari fungsi berikut yang diterjemahkan 4 satuan ke kanan: <\/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>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Sebelum menghitung fungsi simetris, terlebih dahulu kita harus memindahkan fungsi tersebut 4 satuan ke kanan, maka: <\/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\"> Dan setelah kita memindahkan fungsinya, kita menghitung fungsi simetris terhadap sumbu X. Untuk melakukan ini, kita harus meniadakan fungsi yang diperoleh: <\/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\"> Singkatnya, fungsi setelah menerapkan semua operasi dasar adalah: <\/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\">Latihan 5<\/h3>\n<p> Geser fungsi berikut 2 satuan ke kiri, lalu perluas secara vertikal sebanyak 4 kali: <\/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>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Pertama, kita pindahkan fungsinya dua satuan ke kiri: <\/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\"> Dan kemudian kita perluas fungsinya sepanjang sumbu Y dengan faktor 4: <\/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\"> Kesimpulannya, fungsi setelah menerapkan semua transformasi dasar adalah: <\/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\">Latihan 6<\/h3>\n<p> Dari fungsinya<\/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> tentukan representasi mana pada grafik yang sesuai dengan fungsi tersebut <\/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=\"latihan diselesaikan langkah demi langkah pada transformasi fungsi\" 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>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Fungsi<\/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> adalah fungsinya<\/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> turun 3 unit. Karena dengan mengurangkan suatu bilangan dari suatu fungsi, Anda menurunkan fungsi tersebut.<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, representasi dari<\/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> sesuai dengan <strong>garis b)<\/strong> , karena digeser ke bawah sebanyak 3 satuan dibandingkan dengan<\/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\"> Hal ini dapat dilihat dengan melihat sumbu vertikal: kapan<\/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> melewati 0, garis merah melewati -3, sehingga digeser ke bawah 3 satuan.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 7<\/h3>\n<p> Dari fungsinya<\/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> tentukan parabola mana yang merupakan representasi fungsi tersebut <\/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=\"menyelesaikan masalah transformasi fungsi\" 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>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Fungsi<\/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> adalah fungsinya<\/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> berpindah 6 unit ke kanan. Kita dapat memverifikasi ini dengan menghitung <\/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\"> Oleh karena itu, representasi dari<\/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> sesuai dengan <strong>parabola c)<\/strong> , karena digeser 6 satuan ke kanan dibandingkan dengan<\/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> .<\/p>\n<p class=\"has-text-align-left\"> Hal ini dapat dilihat dengan melihat titik sudut parabola: jarak antara titik sudut parabola<\/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> dan titik puncak parabola c) berjumlah 6 satuan, maka titik puncak parabola c) digeser ke kanan sebanyak 6 satuan dibandingkan yang pertama.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Halaman ini menjelaskan apa itu transformasi fungsi dan cara menemukannya. Ada tiga jenis transformasi: translasi (atau perpindahan), simetri, dan ekspansi (atau kontraksi). Anda juga akan menemukan latihan diselesaikan langkah demi langkah sehingga Anda dapat berlatih dan memahami konsep tanpa meninggalkan keraguan. Apa yang dimaksud dengan transformasi fungsi? Terkadang kita mungkin diminta untuk membuat grafik fungsi &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/pembagian-monoma-membagi-contoh-dan-latihan-yang-diselesaikan-1\/\"> <span class=\"screen-reader-text\">Transformasi fungsi: terjemahan, simetri, ekspansi dan kompresi<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[49],"tags":[],"class_list":["post-13","post","type-post","status-publish","format-standard","hentry","category-representasi-fungsi"],"yoast_head":"<!-- This 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