{"id":358,"date":"2023-07-04T20:36:38","date_gmt":"2023-07-04T20:36:38","guid":{"rendered":"https:\/\/mathority.org\/id\/fungsi-proporsionalitas-terbalik\/"},"modified":"2023-07-04T20:36:38","modified_gmt":"2023-07-04T20:36:38","slug":"fungsi-proporsionalitas-terbalik","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/fungsi-proporsionalitas-terbalik\/","title":{"rendered":"Fungsi proporsionalitas terbalik"},"content":{"rendered":"<p>Halaman ini menjelaskan apa itu fungsi proporsionalitas terbalik dan cara membuat grafiknya. Selain itu, Anda akan menemukan semua karakteristik fungsi jenis ini, cara menghitung domainnya, dan juga beberapa contoh serta latihan yang diselesaikan langkah demi langkah untuk latihan. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-de-proporcionalidad-inversa\"><\/span> Apa yang dimaksud dengan fungsi proporsionalitas terbalik? <span class=\"ez-toc-section-end\"><\/span><\/h2>\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>Fungsi proporsionalitas terbalik<\/strong> adalah fungsi yang menghubungkan dua besaran yang berbanding terbalik, yaitu besaran yang satu bertambah sedangkan besaran yang lain berkurang dan sebaliknya. Secara umum, fungsi proporsionalitas terbalik didefinisikan dengan rumus 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-0347a755f31ebb9b48b58bae6f6b57ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{k}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"46\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Emas<\/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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah konstanta yang disebut rasio proporsionalitas.<\/p>\n<\/div>\n<p> Jadi, fungsi proporsionalitas terbalik selalu terdiri dari pecahan yang penyebutnya polinomial derajat pertama. Oleh karena itu, mereka adalah jenis fungsi rasional.<\/p>\n<p> Contoh fungsi proporsionalitas terbalik:<\/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-38f2b1957624503310fe6098a8982361_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{5}{x} \\qquad y=\\cfrac{-4}{x}\\qquad y=\\cfrac{2}{x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"257\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Umumnya<\/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-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> umumnya merupakan variabel bebas dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> variabel terikat, atau dengan kata lain variabel<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> bergantung pada<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9cc293b28f198c32e0356b52e2e23bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sebaliknya, perbandingan proporsionalitas (suku pembilangnya) bisa positif atau negatif dan tandanya menandai kenaikan atau penurunan fungsi:<\/p>\n<ul>\n<li> Jika konstan\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> negatif, fungsinya meningkat.<\/li>\n<li> Sebaliknya jika konstan\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> positif maka fungsinya menurun. <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-343\">\n<div class=\"wp-block-column is-layout-flow\">\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-augmentation-inverse-proportionnalite-fonction.webp\" alt=\"contoh peningkatan fungsi proporsionalitas terbalik\" class=\"wp-image-163\" width=\"257\" height=\"336\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\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-fonction-de-proportionnalite-inverse-decroissante.webp\" alt=\"contoh penurunan fungsi proporsionalitas terbalik\" class=\"wp-image-164\" width=\"287\" height=\"335\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<p> Seperti yang Anda lihat, grafik fungsi proporsionalitas terbalik selalu <strong>terdiri dari dua hiperbola<\/strong> yang bergantung pada tanda <em>k<\/em> , akan berada di satu kuadran atau kuadran lainnya. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"dominio-de-una-funcion-de-proporcionalidad-inversa\"><\/span> Domain fungsi proporsionalitas terbalik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sebagai salah satu jenis fungsi rasional, <strong>domain dari fungsi proporsionalitas terbalik adalah semua bilangan real kecuali bilangan yang hilang dari penyebutnya<\/strong> . Karena penyebutnya tidak akan pernah nol karena akan menghasilkan bilangan tak terhingga.<\/p>\n<p> Sebagai contoh, kita akan menentukan domain dari fungsi proporsionalitas terbalik 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-2ed569638a8112040c8eb65917144a99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= \\cfrac{4}{x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Untuk mengetahui kapan penyebutnya nol, kita harus menyamakan ekspresinya dengan 0 dan menyelesaikan persamaannya:<\/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-2a57ca6c48b6f646aeb64eb7f05e4840_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" 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-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Jadi, ketika x bernilai 1, penyebutnya akan menjadi nol dan kita memperoleh ketidakpastian. Jadi domain dari fungsi tersebut adalah semua bilangan real dikurangi <\/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-29163feacef7bfd88b9b5d136f8fef91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=1.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" 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-05c8e4a398e9bca8582fa539c89426fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}-\\{ 1 \\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"has-text-align-left wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-representar-una-funcion-de-proporcionalidad-inversa\"><\/span> Cara Membuat Grafik Fungsi Proporsionalitas Terbalik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Kita akan melihat cara membuat grafik fungsi proporsionalitas terbalik menggunakan sebuah contoh.<\/p>\n<ul>\n<li> Kami akan mewakili fungsi berikut dalam grafik:<\/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-664a33c2348cf355b5ae0b6c98be57b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{3}{x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Hal pertama yang perlu kita lakukan adalah mencari domain dari fungsi tersebut. Sebagai pecahan, penyebutnya tidak boleh 0 karena akan menghasilkan bilangan tak terhingga. Oleh karena itu, domainnya akan semuanya x kecuali penyebutnya dibatalkan.<\/p>\n<p> Oleh karena itu, kami menetapkan penyebutnya sama dengan 0 untuk melihat x mana yang tidak termasuk dalam domain:<\/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-e0aacb848a27943fc0e8fba70f545d78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" 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-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, domain dari fungsi tersebut adalah semua bilangan kecuali 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-298deba50795b5fc3979441d68ef3ed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{2\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Setelah kami mengetahui nomor mana yang bukan milik domain, kami membuat tabel nilai. Untuk merepresentasikan fungsi proporsionalitas terbalik, perlu menghitung 3 atau 4 titik di kiri dan 3 atau 4 titik di kanan bilangan yang tidak termasuk dalam domain (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-664a33c2348cf355b5ae0b6c98be57b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{3}{x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" 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-f03d2c89a0898c906173bba4a7e16699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; y \\\\ \\hline 3 &amp; 3 \\\\ 4 &amp; 1,5 \\\\ 5 &amp; 1 \\\\ 6 &amp; 0,75 \\\\ 1 &amp; -3 \\\\ 0 &amp; -1,5 \\\\  -1 &amp; -1 \\\\ -2 &amp; -0,75\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"200\" width=\"104\" style=\"vertical-align: -95px;\"><\/p>\n<\/p>\n<p> Sekarang mari kita nyatakan titik-titik pada grafik <strong>:<\/strong> <\/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\/comment-representer-les-fonctions-de-proportionnalite-inverse.webp\" alt=\"cara merepresentasikan fungsi proporsionalitas terbalik\" class=\"wp-image-165\" width=\"531\" height=\"533\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Dan akhirnya kita gabungkan titik-titiknya, membentuk dua hiperbola dari fungsi proporsionalitas terbalik. Selain itu, kami memanjangkan cabang-cabang hiperbola untuk menunjukkan bahwa mereka terus tumbuh: <\/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\/representation-graphique-dune-fonction-de-proportionnalite-inverse.webp\" alt=\"representasi grafis dari fungsi proporsionalitas terbalik\" class=\"wp-image-166\" width=\"531\" height=\"537\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Perhatikan bahwa fungsinya mendekati<\/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-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> , baik di kanan maupun di kiri. Akan tetapi, ia tidak pernah mencapai angka 2, ia sangat dekat namun tidak pernah mengenainya. JADI,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> itu adalah <strong>asimtot vertikal<\/strong> . Ini karena<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> tidak termasuk dalam domain fungsi tersebut dan oleh karena itu, fungsi tersebut tidak ada pada titik tersebut.<\/p>\n<p> Dan hal yang sama terjadi pada sumbu X horizontal. Fungsinya mendekati<\/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-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\"><\/p>\n<p> tapi jangan pernah menyentuhnya. Belum,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah <strong>asimtot horizontal<\/strong> .<\/p>\n<p> Artinya semua fungsi proporsionalitas terbalik adalah diskontinu karena selalu mempunyai asimtot.<\/p>\n<p> Anda dapat mempelajari lebih lanjut tentang asimtot dan batasan fungsi di situs web kami. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-funciones-de-proporcionalidad-inversa\"><\/span> Memecahkan masalah fungsi proporsionalitas terbalik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Hitung domain dari fungsi proporsionalitas terbalik 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-e6ee0e8c316d13415956aebdf1f779fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{1}{3x+6}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"85\" style=\"vertical-align: -14px;\"><\/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 solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Fungsi proporsionalitas terbalik tidak akan ada jika penyebutnya 0, karena fungsi tersebut akan menghasilkan \u221e. Oleh karena itu, kita perlu menetapkan penyebut fungsi tersebut sama dengan 0 untuk melihat bahwa x menghilangkan penyebutnya dan, oleh karena itu, tidak termasuk dalam domain. <\/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-711df3e7ed1611e60f6b2a78ce211050_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x+6 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"82\" style=\"vertical-align: -2px;\"><\/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-464bbbde213f977372efa4cdc52fe0ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x = -6\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"66\" 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-67f6a3da67428df0d214fb581e6657db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-6}{3} = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"112\" 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-fbd5fe607cd89a42b4db6e52bc047c56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{-2\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" 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> Gambarkan fungsi proporsionalitas terbalik 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-fd78dd9762960a5337acc3e2d9ea8c8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{3}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"46\" style=\"vertical-align: -12px;\"><\/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 solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Hal pertama yang harus dilakukan adalah menghitung domain 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-64621958dc2faf8135c3f98bef105836_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x =0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" 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-918f34eaaa0d095d88bcaf837d725d34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{ 0 \\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah kita mengetahui nomor mana yang bukan milik domain, kita membuat array nilai dengan 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-004c097530669885cf19e9aa97d07444_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; y \\\\ \\hline 1 &amp; 3 \\\\ 2 &amp; 1,5 \\\\ 3 &amp; 1 \\\\ 4 &amp; 0,75 \\\\ -1 &amp; -3 \\\\ -2 &amp; -1,5 \\\\ -3 &amp; -1 \\\\ -4 &amp; -0,75 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"200\" width=\"104\" style=\"vertical-align: -95px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Terakhir, kita nyatakan titik-titik yang diperoleh pada grafik dan menggambar hiperbola, sehingga membentuk fungsi proporsionalitas terbalik: <\/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\/exercice-resolu-pas-a-pas-de-fonction-de-proportionnalite-inverse.webp\" alt=\"Latihan diselesaikan selangkah demi selangkah dari fungsi proporsionalitas terbalik\" class=\"wp-image-167\" width=\"526\" height=\"530\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 3<\/h3>\n<p> Gambarkan fungsi proporsionalitas terbalik 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-f7d1a2bfde357023677380a9d117c7ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= \\cfrac{-1}{x-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" style=\"vertical-align: -12px;\"><\/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 solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Hal pertama yang harus dilakukan adalah menghitung domain 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-53eaacfeed4d0f3ae6746f40f52edbdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x -3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" 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-07e5375bb6ca82b5198a9e829ba42984_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x =3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" 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-d33d13eb18d8be7473178f63e2b33ea6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{ 3 \\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah kita mengetahui domain fungsinya, kita membuat tabel nilai:<\/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-7d240eeb6b2aa8530035b99a488e039a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; y \\\\ \\hline 3,5 &amp; -2 \\\\ 4 &amp; -1 \\\\ 5 &amp; -0,5 \\\\ 6 &amp; -0,33 \\\\ 2,5 &amp; 2  \\\\ 2 &amp; 1 \\\\ 1 &amp; 0,5 \\\\ 0 &amp; 0,33\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"200\" width=\"107\" style=\"vertical-align: -95px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Terakhir, kami merepresentasikan titik-titik yang diperoleh pada grafik dan memplot hiperbola, sehingga membentuk fungsi proporsionalitas terbalik: <\/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-des-fonctions-de-proportionnalite-inverses.webp\" alt=\"Latihan yang diselesaikan untuk fungsi proporsionalitas terbalik\" class=\"wp-image-168\" width=\"423\" height=\"432\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 4<\/h3>\n<p> Gambarkan fungsi proporsionalitas terbalik 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-18718c6d0a65973fb2830b13e3ef90e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= \\cfrac{4}{2x-4} +1\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"114\" style=\"vertical-align: -12px;\"><\/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 solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Pertama, kita perlu menghitung domain 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-af6694fc6992622f98a8707910f98046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x-4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" 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-4e696d73fad80caf096cb986a3c357b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x =4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" 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-4d1252315e59c0aa8c2cf0296443e4e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x =\\cfrac{4}{2} =2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" 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-bb4b13269ed4b2e103e50983e300dcfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{ 2 \\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah kita mengetahui domain fungsinya, kita membuat array nilai:<\/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-925c625919345d725660e1ccab33c78b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; y \\\\ \\hline 2,5 &amp; 5 \\\\ 3 &amp; 3 \\\\ 4 &amp; 2 \\\\ 6 &amp; 1,5 \\\\ 1,5 &amp; -3  \\\\ 1 &amp; -1 \\\\ 0 &amp; 0 \\\\ -2 &amp; 0,5\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"200\" width=\"84\" style=\"vertical-align: -95px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir, kita nyatakan titik-titik yang diperoleh pada grafik dan gambarkan hiperbolanya, sehingga membentuk fungsi proporsionalitas terbalik: <\/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\/exercice-pour-representer-graphiquement-une-fonction-de-proportionnalite-inverse.webp\" alt=\"latihan membuat grafik fungsi proporsionalitas terbalik\" class=\"wp-image-169\" width=\"509\" height=\"543\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 5<\/h3>\n<p> Gambarkan fungsi rasional 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-379664d569f63739a52aef2f4a3da41b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{2x+3}{2x+6}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"85\" style=\"vertical-align: -14px;\"><\/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 solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Hal pertama yang harus dilakukan adalah menghitung domain 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-eb310e295335d320e66cac6a8a6a3270_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"82\" style=\"vertical-align: -2px;\"><\/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-6b254eeeabf14c903b414b7f844bcd54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x =-6\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"66\" 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-be0dac801e36b79ec2bac9a5be70ad7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x =\\cfrac{-6}{2} =-3\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"113\" 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-3eb9671adf4127bd8129820378cb2a44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{ -3 \\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah kita mengetahui domain fungsinya, kita membuat tabel nilai:<\/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-5dfd65f4a7fca984bdc6f16ec89154c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; y \\\\ \\hline -2,5 &amp; -2 \\\\ -2 &amp; -0,5 \\\\ -1 &amp; 0,25 \\\\ 1 &amp; 0,63 \\\\ -3,5 &amp; 4  \\\\ -4 &amp; 2,5 \\\\ -5 &amp; 1,75 \\\\ -7 &amp; 1,38\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"200\" width=\"112\" style=\"vertical-align: -95px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Untuk menyelesaikannya, cukup nyatakan titik-titik yang diperoleh pada grafik dan gambarkan hiperbolanya, sehingga membentuk fungsi pecahan: <\/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\/fonction-de-proportionnalite-inverse.webp\" alt=\"fungsi proporsionalitas terbalik\" class=\"wp-image-170\" width=\"545\" height=\"460\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-funcion-de-proporcionalidad-inversa\"><\/span> Penerapan fungsi proporsionalitas terbalik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Fungsi proporsionalitas terbalik muncul dalam banyak kasus dalam fisika dan matematika.<\/p>\n<p> Misalnya, digunakan untuk menggambarkan hubungan antara tekanan dan volume dalam gas ideal yang suhunya konstan k. Fungsi ini disebut hukum Boyle-Mariotte (P\u00d7V=k) dan merupakan contoh fungsi proporsionalitas terbalik. Jelasnya, domain definisi fungsi ini terbatas hanya pada cabang positif, karena tidak ada volume atau tekanan negatif.<\/p>\n<p> Hubungan antara intensitas arus dan hambatan listrik dengan beda potensial konstan juga diatur oleh fungsi proporsionalitas terbalik. Fungsi ini dikenal sebagai hukum Ohm (V=I\u00d7R).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Halaman ini menjelaskan apa itu fungsi proporsionalitas terbalik dan cara membuat grafiknya. Selain itu, Anda akan menemukan semua karakteristik fungsi jenis ini, cara menghitung domainnya, dan juga beberapa contoh serta latihan yang diselesaikan langkah demi langkah untuk latihan. Apa yang dimaksud dengan fungsi proporsionalitas terbalik? Fungsi proporsionalitas terbalik adalah fungsi yang menghubungkan dua besaran yang &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/fungsi-proporsionalitas-terbalik\/\"> <span class=\"screen-reader-text\">Fungsi proporsionalitas terbalik<\/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-358","post","type-post","status-publish","format-standard","hentry","category-representasi-fungsi"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Fungsi proporsionalitas terbalik - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/fungsi-proporsionalitas-terbalik\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fungsi proporsionalitas terbalik - Mathority\" \/>\n<meta property=\"og:description\" content=\"Halaman ini menjelaskan apa itu fungsi proporsionalitas terbalik dan cara membuat grafiknya. 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