{"id":25,"date":"2023-09-17T11:05:21","date_gmt":"2023-09-17T11:05:21","guid":{"rendered":"https:\/\/mathority.org\/id\/fungsi-rasional\/"},"modified":"2023-09-17T11:05:21","modified_gmt":"2023-09-17T11:05:21","slug":"fungsi-rasional","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/fungsi-rasional\/","title":{"rendered":"Fungsi rasional"},"content":{"rendered":"<p>Di sini Anda akan menemukan apa itu fungsi rasional. Selain itu, kami menjelaskan cara menghitung domain dan asimtot fungsi rasional. Dan tidak hanya itu, Anda akan melihat apa saja ciri-ciri fungsi rasional. Terakhir, Anda dapat berlatih dengan latihan langkah demi langkah tentang fungsi rasional. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-racional\"><\/span> Apa yang dimaksud dengan fungsi rasional?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Pengertian fungsi rasional adalah sebagai berikut:<\/p>\n<p> <strong>Fungsi rasional adalah fungsi yang dibentuk oleh hasil bagi dua polinomial<\/strong> , yaitu fungsi rasional adalah pecahan yang pembilang dan penyebutnya mempunyai polinomial.<\/p>\n<p> Fungsi rasional dicirikan oleh singularitas pada titik di mana penyebutnya hilang.<\/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-a80ec33ef964f9463287fb8c93605b34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{a_0+a_1x+a_2x^2+\\dots +a_nx^n}{b_0+b_1x+b_2x^2+\\dots +n_nx^n}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"285\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> Fungsi rasional disebut juga fungsi pecahan.<\/p>\n<p> Di sisi lain, fungsi rasional tidak sama dengan fungsi irasional. Fungsi irasional (atau radikal) adalah fungsi yang terdiri dari akar-akar.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-funciones-racionales\"><\/span> Contoh Fungsi Rasional<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Untuk lebih memahami pengertian fungsi rasional, kita akan melihat beberapa contoh fungsi jenis ini.<\/p>\n<ul>\n<li> <u style=\"text-decoration-color:#FF9B28;\">Fungsi rasional dengan polinomial derajat pertama pada pembilang dan penyebutnya:<\/u><\/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-b170c6c49759eeb2d1d3f81bbf0ebfc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x+3}{2x-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"110\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Jenis fungsi rasional ini disebut juga <strong>fungsi homograf<\/strong> .<\/p>\n<ul>\n<li> <u style=\"text-decoration-color:#FF9B28;\">Fungsi rasional dengan konstanta di pembilangnya dan polinomial di penyebutnya:<\/u><\/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-931f934a646a46832b66a8a3efe3ad17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{7}{x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"101\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Jenis fungsi rasional ini disebut <strong>fungsi proporsional terbalik<\/strong> dan digunakan untuk mendefinisikan besaran proporsional terbalik secara matematis.<\/p>\n<ul>\n<li> <u style=\"text-decoration-color:#FF9B28;\">Fungsi rasional dengan polinomial derajat ketiga pada pembilangnya dan polinomial derajat kedua pada penyebutnya:<\/u> <\/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-82bb59d3904629b47192dfd05456a638_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^3+4x^2-2x+6}{x^2+3x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"198\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"dominio-de-una-funcion-racional\"><\/span> Domain fungsi rasional <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px; margin-bottom:30px\">\n<p> Suatu bilangan dibagi 0 merupakan suatu ketidakpastian yang menghasilkan tak terhingga (\u221e), sehingga fungsi rasional akan selalu ada kecuali penyebutnya 0.<\/p>\n<p> Oleh karena itu, <strong>domain fungsi rasional<\/strong> terdiri dari semua bilangan real kecuali nilai yang menghilangkan penyebutnya.<\/p>\n<\/div>\n<p> Jadi, untuk mendapatkan domain dari suatu fungsi rasional, kita perlu mencari kapan penyebutnya 0, karena titik ini adalah satu-satunya titik yang tidak termasuk dalam domain tersebut.<\/p>\n<p> Mari kita lihat bagaimana domain fungsi rasional dihitung dengan menyelesaikan sebuah contoh:<\/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-dc119bb22722de1d946894030ac0e6e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{5x}{x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"101\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Pertama-tama kita atur penyebutnya menjadi 0, lalu kita selesaikan persamaan yang dihasilkan:<\/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-24e301fa7ea2e8d9f0041192d9a84927_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"73\" 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-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, jika x adalah -2, penyebutnya adalah 0 dan fungsinya tidak akan ada. Oleh karena itu, domain fungsi tersebut terdiri dari semua bilangan real kecuali x=-2. Hal ini dinyatakan sebagai 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-c69046d9ec5ea032ce1e6f7f070dbf83_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<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"asintotas-de-una-funcion-racional\"><\/span> Asimtot fungsi rasional<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Salah satu sifat utama fungsi rasional adalah asimtotnya, karena fungsi tersebut menentukan representasi grafisnya.<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/representasi-fungsi\/\">representasi grafis dari suatu fungsi<\/a><\/span><\/p>\n<p> <strong>Asimtot suatu fungsi rasional<\/strong> adalah garis-garis yang didekati grafik fungsi tersebut hingga tak terhingga tetapi tidak pernah menyentuhnya.<\/p>\n<p> Ada tiga jenis asimtot: asimtot vertikal, asimtot horizontal, dan asimtot miring.<\/p>\n<p> Di bawah ini Anda memiliki tiga jenis asimtot yang dapat digambarkan dalam grafik fungsi rasional dengan warna merah.<\/p>\n<p class=\"has-text-align-center\"> <u style=\"text-decoration-color:#E74C3C;\"><strong>Asimtot vertikal dari fungsi rasional<\/strong><\/u> <\/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-dasymptote-verticale.webp\" alt=\"asimtot vertikal dari fungsi rasional\" class=\"wp-image-1294\" width=\"408\" height=\"361\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"> <u style=\"text-decoration-color:#E74C3C;\"><strong>Asimtot horizontal dari fungsi rasional<\/strong><\/u> <\/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-dasymptote-horizontale.webp\" alt=\"asimtot horizontal dari fungsi rasional\" class=\"wp-image-1333\" width=\"478\" height=\"378\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"> <u style=\"text-decoration-color:#E74C3C;\"><strong>Asimtot miring dari fungsi rasional<\/strong><\/u> <\/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\/image-1.png\" alt=\"asimtot miring dari fungsi rasional\" class=\"wp-image-1374\" width=\"386\" height=\"436\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Seperti yang Anda lihat, menentukan asimtot suatu fungsi dari grafiknya cukup sederhana, tetapi menghitung asimtot suatu fungsi rasional tanpa representasi grafiknya cukup rumit. Inilah sebabnya kami menyarankan Anda melihat bagaimana asimtot suatu fungsi dihitung di situs web kami. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-una-funcion-racional\"><\/span> Ciri-ciri fungsi rasional<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Fungsi rasional mempunyai ciri-ciri sebagai 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-9c24e4e9a6871d3e8e07e85c24b039c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{P(x)}{Q(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"98\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\">Seperti yang kita lihat di atas, domain fungsi rasional mencakup semua bilangan real kecuali nilai yang menghilangkan penyebut pecahan.<\/span><\/li>\n<\/ul>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\">Secara umum, rentang (atau rentang) suatu fungsi rasional mencakup semua bilangan real kecuali nilai yang fungsi tersebut memiliki asimtot horizontal.<\/span><\/li>\n<\/ul>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\">Fungsi rasional bersifat kontinu di seluruh domainnya. Atau dengan kata lain, fungsi rasional menunjukkan diskontinuitas pada titik-titik yang tidak termasuk dalam domainnya.<\/span><\/li>\n<\/ul>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\">Representasi grafis dari sebagian besar fungsi rasional terdiri dari dua hiperbola.<\/span><\/li>\n<\/ul>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\">Beberapa aturan asimtot fungsi rasional dapat disimpulkan dari pembilang polinomial.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a80be6e42ac3b3c6528958bbfa21f92c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> dan polinomial penyebutnya <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4d38083076c97f0893079e8fed89adb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<ul style=\"list-style-type:circle;margin-left:10%;color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:15px; margin-top:15px\"> <span style=\"color:#101010;font-weight: normal;\">Suatu fungsi rasional mempunyai asimtot vertikal pada titik-titik yang merupakan akar-akarnya\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8061e215a5d055a2cf14c44c4febfad5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> tapi ini bukan akar dari<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0f6500c41747705211eacbfc8d05aba4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<li style=\"margin-bottom:15px; margin-top:15px\"> <span style=\"color:#101010;font-weight: normal;\">Jika derajat\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a80be6e42ac3b3c6528958bbfa21f92c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> kurang dari derajat<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8061e215a5d055a2cf14c44c4febfad5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<p> , garis y=0 adalah asimtot horizontal dari fungsi rasional.<\/li>\n<li style=\"margin-bottom:15px; margin-top:15px\"> <span style=\"color:#101010;font-weight: normal;\">Jika derajat\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a80be6e42ac3b3c6528958bbfa21f92c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> lebih besar dari derajatnya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8061e215a5d055a2cf14c44c4febfad5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<p> , fungsi rasional tidak memiliki asimtot horizontal.<\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">Jika derajat\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a80be6e42ac3b3c6528958bbfa21f92c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> adalah satuan yang lebih besar dari derajat<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8061e215a5d055a2cf14c44c4febfad5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<p> dan kedua polinomial tersebut tidak mempunyai akar yang sama, fungsi rasional mempunyai asimtot miring. <\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-funciones-racionales\"><\/span> Latihan soal fungsi rasional<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Temukan domain dari 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-94fcabf09d798d56e4d439c3dc4945b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\displaystyle\\frac{4x}{2x+4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"110\" 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 solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Ini adalah fungsi rasional, jadi domainnya terdiri dari semua bilangan kecuali bilangan yang menghilangkan penyebutnya, karena fungsi tersebut akan menghasilkan \u221e.<\/p>\n<p class=\"has-text-align-left\"> Jadi kita menetapkan penyebut bilangan bulat sama dengan nol untuk melihat bilangan 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-198bb8c11e20e5c9864ef9e60a2facc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"82\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami menyelesaikan persamaan yang dihasilkan: <\/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-8bb8c1283df065c83c44b7fe484324a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x=-4\" 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-578104a63c70bc5ba4b685855966f28e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-4}{2}=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"112\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, domain fungsi hanya terdiri dari 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-ee75b8bb1136ab715a80e56e910f1626_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{Dom } \\ \\bm{f = \\mathbb{R}- \\{ -2 \\} }\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"157\" 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> Tentukan titik potong fungsi rasional berikut dengan sumbu kartesius: <\/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-6ef48653e91a2935a9776b62ddd1f25b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^2-9}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"109\" 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 solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> <strong>Titik potong dengan sumbu X<\/strong><\/p>\n<p class=\"has-text-align-left\"> Untuk mencari titik potong fungsi tersebut dengan sumbu X perlu dicari penyelesaiannya <\/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-05bb421b504b7ae4aa483574cd6f28d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" 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-0bce6c022ed0fc63f4659af75888f96c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" 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-603043b6d5768eaace4011208f30bec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2-9}{x}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"81\" 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-0b2fd4733c1dfbb47969d5b92e3e4f04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-9=0\\cdot x\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"104\" 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-ce55adbc277e9378607d68bce8ef19fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-9=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" 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-05112cb5a98f653cd1920fb40e5ef9a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" 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-9cba0400a71268c96427f3b00bf29b6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=\\pm 3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"64\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kita memperoleh dua penyelesaian persamaan kuadrat, sehingga fungsi rasional memotong sumbu absis di dua titik berbeda, yaitu:<\/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-013260528208aa1656c5407fa8e29db9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(3,0)\\qquad (-3,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>Titik potong dengan sumbu Y<\/strong><\/p>\n<p class=\"has-text-align-left\"> Untuk mencari titik potong dengan sumbu Y harus 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-8f92d7beea0ed3a053927c2d429d3450_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" 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-969a7e35c182b2950e797fec58ddab28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0)=\\cfrac{0^2-9}{0}=\\cfrac{-9}{0}= \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"203\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Bilangan apa pun yang dibagi nol merupakan suatu ketidakpastian yang menghasilkan bilangan tak terhingga. Oleh karena itu, fungsi rasional tidak melewati titik mana pun di atas sumbu Y, yaitu tidak mempunyai titik potong dengan sumbu y.<\/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> Gambarkan fungsi rasional berikut pada grafik: <\/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 solusinya<\/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 menggambar fungsi rasionalnya: <\/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, \" data-src=\"\"><\/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> Tentukan asimtot fungsi rasional yang digambarkan di bawah ini: <\/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-representation-limites-infini.webp\" alt=\"asimtot fungsi rasional\" class=\"wp-image-1244\" width=\"403\" height=\"406\" 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\"> Asimtotnya terlihat sangat jelas pada grafik, karena direpresentasikan sebagai garis putus-putus berwarna merah.<\/p>\n<p class=\"has-text-align-left\"> Dalam soal ini, fungsinya sangat dekat dengan garis horizontal y=1 tetapi tidak pernah menyentuhnya. Oleh karena itu, fungsi rasional memiliki satu asimtot horizontal, yaitu y=1.<\/p>\n<p class=\"has-text-align-left\"> Demikian pula, representasi grafis dari fungsi tersebut sangat dekat dengan garis vertikal x=-1 dan x=1, tetapi tidak pernah mencapai nilai tersebut. Oleh karena itu, fungsi rasional memiliki dua asimtot vertikal yang berbeda, yaitu x=-1 dan x=1.<\/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> Hitung semua asimtot 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-ffd06824234d445d38d021cbb04bfa23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{6x-4}{2x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"110\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> <strong>Catatan:<\/strong> Untuk menyelesaikan latihan ini, kami menyarankan Anda terlebih dahulu membuka tautan di atas tentang <u style=\"text-decoration-color:#FF9B28;\">cara menghitung asimtot suatu fungsi<\/u> dan melihat penjelasannya. <\/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\"> <strong><span style=\"text-decoration: underline;\">asimtot vertikal<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\"> Untuk menghitung asimtot vertikal suatu fungsi, pertama-tama kita harus mencari domain fungsi tersebut. Oleh karena itu, kita menetapkan penyebut fungsi rasional sama dengan 0 untuk mencari titik-titik 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-ba1a17401e951a8539e475d758a871d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x +2 =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-b2a522ee7d1c1819c496c45af9549bc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x= -2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" 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-3e60b04854152fc93f76ad6c29e09346_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{-2}{2} = -1\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"112\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, domain fungsi tersebut terdiri dari semua bilangan kecuali -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-09f86d513e25805efa3dbddfc2e0229e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{ -1 \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi x=-1 bisa menjadi asimtot vertikal. Untuk memeriksanya, kita harus menghitung limit fungsi di titik 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-19ee5b45a22b402ee890392a91803649_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -1 } \\frac{6x-4}{2x+2} = \\frac{6\\cdot(-1)-4}{2\\cdot(-1)+2}=\\frac{-10}{0}= \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"311\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, x=-1 adalah asimtot vertikal dari fungsi rasional, karena limit fungsi pada titik ini memberikan tak terhingga.<\/p>\n<p class=\"has-text-align-left\"> <strong><span style=\"text-decoration: underline;\">asimtot horizontal<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\"> Untuk menentukan asimtot horizontal, kita perlu menghitung limit tak terhingga 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-604ce9e6e3a0943003f79d5f890b81d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty}\\frac{6x-4}{2x+2} = \\frac{6(+\\infty)}{2(+\\infty)} = \\frac{+\\infty}{+\\infty} = \\frac{6}{2} = \\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"312\" style=\"vertical-align: -17px;\"><\/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-823441caef29e22ea5cda9685af7c1bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty}\\frac{6x-4}{2x+2} = \\frac{6(-\\infty)}{2(-\\infty)} = \\frac{-\\infty}{-\\infty} = \\frac{6}{2} = \\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"312\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dalam hal ini, hasil batas tak terhingga antara tak terhingga adalah pembagian koefisien x pangkat tertinggi, karena pembilang dan penyebutnya berorde sama.<\/p>\n<p class=\"has-text-align-left\"> Dua limit tak hingga dari fungsi tersebut memberi kita nilai 3, jadi y=3 adalah asimtot horizontal dari fungsi rasional.<\/p>\n<p class=\"has-text-align-left\"> <strong><span style=\"text-decoration: underline;\">asimtot miring<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\"> Karena terdapat asimtot horizontal, maka fungsi rasional tidak mempunyai asimtot miring.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di sini Anda akan menemukan apa itu fungsi rasional. Selain itu, kami menjelaskan cara menghitung domain dan asimtot fungsi rasional. Dan tidak hanya itu, Anda akan melihat apa saja ciri-ciri fungsi rasional. Terakhir, Anda dapat berlatih dengan latihan langkah demi langkah tentang fungsi rasional. Apa yang dimaksud dengan fungsi rasional? Pengertian fungsi rasional adalah sebagai &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/fungsi-rasional\/\"> <span class=\"screen-reader-text\">Fungsi rasional<\/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-25","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 rasional: apa itu, domain, asimtot, grafik, latihan,...<\/title>\n<meta name=\"description\" content=\"Kami menjelaskan apa itu fungsi rasional dan semua karakteristiknya (domain, asimtot, grafik, dll). Dengan latihan yang terselesaikan pada fungsi rasional.\" \/>\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-rasional\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fungsi rasional: apa itu, domain, asimtot, grafik, latihan,...\" \/>\n<meta property=\"og:description\" content=\"Kami menjelaskan apa itu fungsi rasional dan semua karakteristiknya (domain, asimtot, grafik, dll). Dengan latihan yang terselesaikan pada fungsi rasional.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/fungsi-rasional\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T11:05:21+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a80ec33ef964f9463287fb8c93605b34_l3.png\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/fungsi-rasional\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/fungsi-rasional\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Fungsi rasional\",\"datePublished\":\"2023-09-17T11:05:21+00:00\",\"dateModified\":\"2023-09-17T11:05:21+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/fungsi-rasional\/\"},\"wordCount\":1072,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Representasi fungsi\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/fungsi-rasional\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/fungsi-rasional\/\",\"url\":\"https:\/\/mathority.org\/id\/fungsi-rasional\/\",\"name\":\"Fungsi rasional: apa itu, domain, asimtot, grafik, latihan,...\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/#website\"},\"datePublished\":\"2023-09-17T11:05:21+00:00\",\"dateModified\":\"2023-09-17T11:05:21+00:00\",\"description\":\"Kami menjelaskan apa itu fungsi rasional dan semua karakteristiknya (domain, asimtot, grafik, dll). Dengan latihan yang terselesaikan pada fungsi rasional.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/id\/fungsi-rasional\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/id\/fungsi-rasional\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/id\/fungsi-rasional\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Fungsi rasional\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/id\/#website\",\"url\":\"https:\/\/mathority.org\/id\/\",\"name\":\"Mathority\",\"description\":\"Di mana rasa ingin tahu bertemu dengan perhitungan!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/id\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/id\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\",\"name\":\"Tim Mathority\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Tim Mathority\"},\"sameAs\":[\"http:\/\/mathority.org\/id\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Fungsi rasional: apa itu, domain, asimtot, grafik, latihan,...","description":"Kami menjelaskan apa itu fungsi rasional dan semua karakteristiknya (domain, asimtot, grafik, dll). Dengan latihan yang terselesaikan pada fungsi rasional.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/id\/fungsi-rasional\/","og_locale":"id_ID","og_type":"article","og_title":"Fungsi rasional: apa itu, domain, asimtot, grafik, latihan,...","og_description":"Kami menjelaskan apa itu fungsi rasional dan semua karakteristiknya (domain, asimtot, grafik, dll). Dengan latihan yang terselesaikan pada fungsi rasional.","og_url":"https:\/\/mathority.org\/id\/fungsi-rasional\/","article_published_time":"2023-09-17T11:05:21+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a80ec33ef964f9463287fb8c93605b34_l3.png"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"5 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/fungsi-rasional\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/fungsi-rasional\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Fungsi rasional","datePublished":"2023-09-17T11:05:21+00:00","dateModified":"2023-09-17T11:05:21+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/fungsi-rasional\/"},"wordCount":1072,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"articleSection":["Representasi fungsi"],"inLanguage":"id","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/id\/fungsi-rasional\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/fungsi-rasional\/","url":"https:\/\/mathority.org\/id\/fungsi-rasional\/","name":"Fungsi rasional: apa itu, domain, asimtot, grafik, latihan,...","isPartOf":{"@id":"https:\/\/mathority.org\/id\/#website"},"datePublished":"2023-09-17T11:05:21+00:00","dateModified":"2023-09-17T11:05:21+00:00","description":"Kami menjelaskan apa itu fungsi rasional dan semua karakteristiknya (domain, asimtot, grafik, dll). Dengan latihan yang terselesaikan pada fungsi rasional.","breadcrumb":{"@id":"https:\/\/mathority.org\/id\/fungsi-rasional\/#breadcrumb"},"inLanguage":"id","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/id\/fungsi-rasional\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/id\/fungsi-rasional\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/id\/"},{"@type":"ListItem","position":2,"name":"Fungsi rasional"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/id\/#website","url":"https:\/\/mathority.org\/id\/","name":"Mathority","description":"Di mana rasa ingin tahu bertemu dengan perhitungan!","publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/id\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"id"},{"@type":"Organization","@id":"https:\/\/mathority.org\/id\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/id\/","logo":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38","name":"Tim Mathority","image":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Tim Mathority"},"sameAs":["http:\/\/mathority.org\/id"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/25","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/comments?post=25"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/25\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/media?parent=25"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/categories?post=25"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/tags?post=25"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}