{"id":24,"date":"2023-09-17T11:06:22","date_gmt":"2023-09-17T11:06:22","guid":{"rendered":"https:\/\/mathority.org\/id\/kontinuitas-fungsi-kontinuitas-suatu-fungsi\/"},"modified":"2023-09-17T11:06:22","modified_gmt":"2023-09-17T11:06:22","slug":"kontinuitas-fungsi-kontinuitas-suatu-fungsi","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/kontinuitas-fungsi-kontinuitas-suatu-fungsi\/","title":{"rendered":"Fungsi kontinu (kontinuitas suatu fungsi)"},"content":{"rendered":"<p>Pada artikel kali ini kami akan menjelaskan apa itu fungsi kontinu dan cara menentukan kontinuitas suatu fungsi di suatu titik atau tidak. Selain itu, Anda akan menemukan properti fungsi kontinu dan analisis kontinuitas fungsi paling umum. Terakhir, Anda dapat berlatih dengan latihan yang diselesaikan pada fungsi kontinu untuk memahami konsep sepenuhnya. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-continua\"><\/span> Apa yang dimaksud dengan fungsi kontinu?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Kontinuitas suatu fungsi dapat dipelajari secara grafis. <strong>Fungsi kontinu adalah fungsi yang dapat direpresentasikan dalam grafik tanpa perlu mengeluarkan pensil dari kertas.<\/strong><\/p>\n<p class=\"has-text-align-center has-medium-font-size\"> <u style=\"text-decoration-color:#FF9B28;\"><strong>Fungsi berkelanjutan<\/strong><\/u> <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fonction-continue.webp\" alt=\"fungsi berkelanjutan\" class=\"wp-image-1491\" width=\"354\" height=\"255\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p> Fungsi di atas bersifat kontinu karena dapat digambar dalam satu goresan tanpa perlu mengangkat tangan dari kertas.<\/p>\n<p> Sebaliknya, jika kondisi kontinuitas sebelumnya tidak dimasukkan ke dalam suatu fungsi, maka disebut <strong>fungsi diskontinyu<\/strong> .<\/p>\n<p class=\"has-text-align-center has-medium-font-size\"> <u style=\"text-decoration-color:#FF9B28;\"><strong>Fungsi terputus-putus<\/strong><\/u> <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fonction-pointillee.webp\" alt=\"fungsi terputus-putus\" class=\"wp-image-1495\" width=\"354\" height=\"262\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p> Fungsi sebelumnya terputus-putus karena untuk merepresentasikannya harus membuat dua garis dengan pensil. Dalam hal ini, fungsi tersebut tidak lagi kontinu di x=3, oleh karena itu kita katakan bahwa x=3 adalah <strong>titik diskontinuitas<\/strong> .<\/p>\n<p> Selain itu, ada tiga <strong>jenis diskontinuitas<\/strong> : diskontinuitas yang dapat dihindari, diskontinuitas lompat hingga yang tak terelakkan, dan diskontinuitas lompat tak terelakkan. Di tautan berikut Anda dapat melihat seperti apa masing-masing jenis diskontinuitas dan apa perbedaannya:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/\">jenis diskontinuitas<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"continuidad-de-una-funcion-en-un-punto\"><\/span> Kontinuitas suatu fungsi pada suatu titik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita melihat seperti apa grafik fungsi kontinu, kita akan melihat cara mengetahui apakah suatu fungsi kontinu atau tidak secara analitis.<\/p>\n<p> Secara matematis, <strong>suatu fungsi kontinu di suatu titik jika memenuhi tiga syarat berikut:<\/strong><\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;border:\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Fungsinya ada pada titik ini, yaitu bayangan titik tersebut ada.<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e7292d399b69758819eab74a2aa9afd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\exists \\ f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"48\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Ada batasan fungsi pada saat ini. Oleh karena itu, batas lateral kiri dan kanan fungsi pada titik ini adalah sama.<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7c4c9431d93839b2511a56583101db46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) = \\lim_{x \\to a^+} f(x)  \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black} \\quad \\exists \\lim_{x \\to a} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"413\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Bayangan suatu titik berimpit dengan limit fungsi pada titik tersebut.<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da2902aa458fe8a9c8234e2be38336c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(a)=\\lim_{x \\to a} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"123\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/ol>\n<p> Jadi, jika ketiga syarat kontinuitas terpenuhi di semua titik suatu fungsi, maka fungsi tersebut kontinu.<\/p>\n<p> Sebagai contoh, kita akan menganalisis kontinuitas fungsi perataan berikut: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/continuite-dune-fonction-definie-par-morceaux.webp\" alt=\"kontinuitas suatu fungsi yang ditentukan sedikit demi sedikit\" class=\"wp-image-201\" width=\"440\" height=\"306\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p> Bahkan jika Anda mengubah bagian, pada intinya<\/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> Fungsi tersebut kontinu, karena batas lateral fungsi pada titik ini sama dan lebih bertepatan dengan nilai fungsi pada titik ini.<\/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-3f659d88902824c6a762a5ebe2d6db14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{x \\to -2^-} f(x)=\\lim\\limits_{x \\to -2^+} f(x)= f(-2)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"300\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Sebaliknya, fungsi tersebut tidak kontinu di suatu titik<\/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-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p> karena kedua batas lateralnya berbeda sehingga limit fungsinya tidak ada pada titik ini:<\/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-5f9d62d0c5ddcefe8cc4cbe2daaf6d57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{x \\to 4^-} f(x)=3 \\neq \\lim\\limits_{x \\to 4^+} f(x)= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"240\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Singkatnya, fungsi yang didefinisikan oleh potongan-potongan tersebut kontinu di semua bilangan real kecuali di<\/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-9ad850560a1ff3e3bb4386cf732d0220_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=4,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\"><\/p>\n<p> dimana terdapat diskontinuitas.<\/p>\n<p> Kami juga dapat memverifikasi bahwa fungsi tersebut terputus-putus<\/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-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p> karena untuk merepresentasikannya secara grafis, pensil harus dikeluarkan dari kertas pada saat ini. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"continuidad-de-funciones-elementales\"><\/span> Kontinuitas fungsi dasar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Jenis fungsi tertentu bersifat kontinu berdasarkan karakteristiknya:<\/p>\n<ul>\n<li> <strong>Fungsi konstanta<\/strong> kontinu pada semua bilangan real.<\/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-252f9958e223f77bf50cb3b92a7c3e35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Fungsi polinomial<\/strong> kontinu untuk semua bilangan real.<\/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-3094a01ff9b10acb7c44349cda083025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=a_0+a_1x+a_2x^2+a_3x^3+\\dots+a_nx^n\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"338\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Fungsi rasional (atau pecahan)<\/strong> kontinu pada semua bilangan real kecuali pada nilai yang menghilangkan penyebut pecahan, pada titik tersebut fungsi tersebut menyajikan diskontinuitas.<\/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-6cc33f4306e45701e8bc92457779201d_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=\"93\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Fungsi eksponensial<\/strong> kontinu pada semua bilangan real:<\/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-73aa6cf687ce5e8c2f9faf41f5614e53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=a^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Fungsi logaritma<\/strong> kontinu di semua titik yang argumennya positif.<\/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-d94badc2befa1e0c57a867970b1040aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a (x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Kontinuitas <strong>fungsi irasional<\/strong> , atau fungsi dengan akar, bergantung pada indeks akar (n). Jika indeksnya genap, ini adalah fungsi kontinu di semua titik yang membuat argumen akar sama dengan atau lebih besar dari nol. Tetapi jika indeksnya ganjil, maka keduanya merupakan fungsi kontinu pada semua bilangan real.<\/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-ca6c3302aac609e9214e62444cfec2bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Kontinuitas <strong>fungsi trigonometri<\/strong> bergantung pada jenis fungsinya. Fungsi sinus dan fungsi kosinus kontinu pada himpunan bilangan real, tetapi fungsi tangennya diskontinu pada titik-titiknya.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0c1c82b94111254bf0771af43a5b4411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x=\\frac{\\pi}{2}+k\\pi\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"91\" style=\"vertical-align: -12px;\"><\/p>\n<p> (di mana <em>k<\/em> adalah bilangan bulat). <\/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-a42292efae266c09baade046e8a3cb76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=sen(x)\\qquad f(x)=cos(x)\\qquad f(x)=tg(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-las-funciones-continuas\"><\/span> Sifat-sifat fungsi kontinu<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sean<\/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-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> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a5054ad96fb0978182340eb214bb125_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"><\/p>\n<p> dua fungsi kontinu pada suatu titik<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c20f4d749ca0651113257e1f1ea66b02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=a,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: -4px;\"><\/p>\n<p> Berikutnya:<\/p>\n<ul>\n<li> <strong>Jumlah dua fungsi kontinu<\/strong> di suatu titik merupakan fungsi kontinu lainnya di titik tersebut.<\/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-c566932a59271b6e33a784bcf81ee749_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)+g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Hasil kali dua fungsi kontinu<\/strong> di suatu titik sama dengan fungsi kontinu lainnya di titik tersebut.<\/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-d47b381826b8c5e901bf202b6d4b14c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\cdot g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Membagi dua fungsi kontinu<\/strong> pada suatu titik akan menghasilkan fungsi kontinu lainnya pada titik tersebut, selama titik tersebut tidak menghilangkan fungsi pembagian tersebut.<\/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-5962b35380c55e0089deeac0a98b01fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{f(x)}{g(x)}\\qquad g(a)\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Susunan dua fungsi kontinu<\/strong> pada suatu titik menimbulkan fungsi kontinu pada titik yang sama.<\/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-ba04f43c8995b3659a05f370a10485a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\circ g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/komposisi-fungsi-fungsi-komposit\/\">apa itu fungsi komposit?<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-continuidad-de-una-funcion\"><\/span> Latihan soal kesinambungan suatu fungsi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Temukan diskontinuitas fungsi yang ditunjukkan pada grafik berikut. Tentukan juga jenis diskontinuitasnya. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-discontinuites-de-fonctions.webp\" alt=\"latihan menyelesaikan diskontinuitas fungsi\" class=\"wp-image-1433\" width=\"400\" height=\"344\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p> <strong>Catatan:<\/strong> untuk melakukan latihan ini kami menyarankan Anda terlebih dahulu melihat apa saja jenis-jenis diskontinuitas dan bagaimana cara mengidentifikasinya. Penjelasannya dapat Anda lihat pada tautan prinsip <u style=\"text-decoration-color:#FF9B28;\">tipe diskontinuitas<\/u> . <\/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 menggambar fungsinya Anda harus menaikkan pensil di x=-2, di x=1 dan di x=4. Oleh karena itu, fungsinya terputus-putus pada ketiga titik ini.<\/p>\n<p class=\"has-text-align-left\"> Pada x=-2, limit ruas kirinya adalah +\u221e dan limit ruas kanannya adalah 3. Jadi, karena salah satu limit sisinya tidak terhingga, fungsi tersebut mempunyai diskontinuitas lompat tak terhingga pada x=-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-eff79ace33659ceb8203e6e27f38fe35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2^-} f(x) = +\\infty \\ \\neq \\ \\lim_{x \\to -2^+} f(x) = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"296\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Limit fungsi di x=1 adalah 0 dan, sebaliknya, nilai fungsi di x=1 sama dengan 2. Oleh karena itu, fungsi tersebut menyajikan diskontinuitas yang dapat dihindari di x=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-3a616cc5210984ffeed3525a219dd53a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1^-} f(x) =   \\lim_{x \\to 1^+} f(x) = 0 \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to 1} f(x) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"350\" style=\"vertical-align: -14px;\"><\/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-61593bab94da601722d6ae7aedfdb172_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1} f(x) =  0 \\neq  f(0) = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"187\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Pada x = 4, limit ruas kirinya adalah -3 dan limit ruas kanannya adalah 1. Oleh karena itu, karena kedua limit sisi tersebut berbeda dan tidak ada satu pun yang menghasilkan tak terhingga, maka fungsi tersebut pasti memiliki diskontinuitas lompatan berhingga di x =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-b758745a987f927350b2d885009c3a87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 4^-} f(x) = -3 \\ \\neq \\ \\lim_{x \\to 4^+} f(x) = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"265\" style=\"vertical-align: -14px;\"><\/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-titik di mana fungsi yang ditunjukkan pada grafik berikut diskontinu. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-types-de-discontinuites-d-une-fonction.webp\" alt=\"menyelesaikan latihan tentang jenis-jenis diskontinuitas suatu fungsi\" class=\"wp-image-1435\" width=\"515\" height=\"434\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\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\"> Pada titik x=6 fungsinya terputus karena terdapat titik terbuka. Limit saat x mendekati 6 adalah -1,4 tetapi f(6)=1. Oleh karena itu, fungsi tersebut mempunyai diskontinuitas yang dapat dihindari pada x=6 karena nilai limitnya tidak sesuai dengan nilai 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-33612be383c71fea04c8c886710f7f10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l} \\displaystyle \\lim_{x \\to 6^-} f(x)=-1,4\\\\[3ex] \\displaystyle \\lim_{x \\to 6^+} f(x)=-1,4 \\end{array} \\right\\} \\bm{\\longrightarrow} \\lim_{x \\to 6} f(x)=-1,4\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"326\" 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-647b9aea6cc8b605d7e8bc7d5e83ee64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 6} f(x)=-1,4 \\neq f(6)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"217\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Pada x=-3 batas lateralnya tidak berimpit dan tidak ada yang menghasilkan tak terhingga. Oleh karena itu, fungsi tersebut memiliki diskontinuitas lompatan terbatas yang tak terelakkan pada x=-3.<\/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-3f7d2a2c7abbc525adfcc7576b449f1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -3^-} f(x)=-2 \\neq \\lim_{x \\to -3^+} f(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"275\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan yang terakhir, fungsi tersebut mempunyai diskontinuitas lompatan tak terhingga pada x = 3, karena setidaknya satu batas lateral pada titik ini menghasilkan tak terhingga. <\/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-89bdb1598b6153cec4e9efce7b0927b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x)=+\\infty \\qquad \\lim_{x \\to 3^+} f(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"300\" style=\"vertical-align: -14px;\"><\/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> Analisislah kontinuitas 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-59ee18262fd6f3427ebab6ceabb22868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\frac{2}{x-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"101\" 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\"> Fungsi rasional kontinu di seluruh domainnya, yaitu di semua bilangan real kecuali nilai yang menghilangkan penyebutnya. Oleh karena itu, kita menetapkan penyebut fungsi rasional sama dengan nol untuk melihat titik 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-845b4cbd750afedb8e09b0ed6a9809c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" 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-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" 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-96a28ea816d10d62e90dd13ad1aa79c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{5\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, fungsi tersebut kontinu di semua titik kecuali x=5.<\/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> Analisislah kontinuitas fungsi perataan 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-a18e6289d268e6ea9fe1ee3ea14d31fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left\\{ \\begin{array}{lcl} 5x-2 &amp; \\text{si} &amp;  x < 1 \\\\[2ex] x^2+2 &amp; \\text{si} &amp; x \\geq 1 \\end{array} \\right.\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"218\" style=\"vertical-align: 0px;\"><\/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\"> Fungsinya juga kontinu di bagian pertama,<\/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-e05d9a74362639e610acff0ab2d83b16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<p> , seperti pada bagian kedua,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-79baa9dfae33805a8e2362cc182fd867_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"47\" style=\"vertical-align: -2px;\"><\/p>\n<p> , karena merupakan fungsi polinomial.<\/p>\n<p class=\"has-text-align-left\"> Jadi, satu-satunya titik di mana suatu fungsi dapat diskontinu adalah titik di mana fungsi tersebut terputus sebagian. Jadi mari kita hitung batas lateral pada titik ini: <\/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-3c84a263e22011d5c8d67c9ee977f98e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1^-} f(x) = \\lim_{x \\to 1} (5x-2)=5\\cdot 1-2=\\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"309\" style=\"vertical-align: -14px;\"><\/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-a1d1b6f5e109c06114b9e36af6f7078a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1^+} f(x) = \\lim_{x \\to 1} (x^2+2)=1^2+2=\\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"293\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kedua limit lateralnya berimpit, limit fungsi ketika x cenderung 1 sama dengan 3:<\/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-a621c7ef999aae5418c2f71da1da67f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1^-} f(x) = \\lim_{x \\to 1^+} f(x) = 3 \\ \\bm{\\longrightarrow} \\ \\exists \\lim_{x \\to 1} f(x) = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"360\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Selanjutnya bayangan x=1 juga 3:<\/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-61f3e46233f15d71b39af62ae6bfb4eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=1^2+2=\\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, karena limit fungsi di x=1 sama dengan bayangan titik tersebut, maka fungsi tersebut kontinu di titik x=1. Oleh karena itu, bilangan ini kontinu pada semua bilangan real. <\/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-8cb4559dfddcda3b3c68a5d64eeadcee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(1)=\\lim_{x \\to 1} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"122\" style=\"vertical-align: -12px;\"><\/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> Pelajari kesinambungan fungsi irasional 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-c43021550a231793494acc2b6eea24d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{2x+6}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" 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\"> Merupakan fungsi radikal yang indeksnya genap, sehingga fungsi tersebut akan kontinu selama argumen akarnya lebih besar dari 0 (karena akar kuadrat dari suatu bilangan negatif tidak ada):<\/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-d54da4e00c0cc48d43914e9e34b1c1d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+6\\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menyelesaikan pertidaksamaan: <\/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-7739f2163d650971be01af6f5a93ae25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x\\ge -6\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"66\" style=\"vertical-align: -3px;\"><\/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-db29954e4e5815cd2bf4bcbfe4c53145_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\ge \\cfrac{-6}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"67\" 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-dfc84780b14328431bcc372ff904772d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\ge -3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Penyelesaiannya terdiri dari semua bilangan yang lebih besar atau sama dengan -3. Oleh karena itu, fungsi tersebut kontinu pada interval domainnya: <\/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-1d2a6678926adfe02dc663e155ec573f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{Dom } \\ \\bm{f = [-3,+\\infty) }\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" 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 6<\/h3>\n<p> Analisislah kontinuitas fungsi logaritma 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-e2c2073b5212610fcc153bdb47eacccf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_3 (-3x+6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" 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\"> Ini adalah fungsi logaritma, dan tidak ada logaritma bilangan negatif maupun logaritma 0. Oleh karena itu, fungsi tersebut akan ada selama argumen logaritmanya positif (lebih besar dari nol):<\/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-53c23d1b367425e8cfb94fb36235b8f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3x+6>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;95&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menyelesaikan pertidaksamaan: <\/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-d0183470903eba7ebd08dfcdbf49287e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3x>-6&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;78&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/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-9c67175fd587232ef7d927f7dfca725f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x<\\cfrac{-6}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"67\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ingatlah bahwa ketika suatu bilangan negatif dibagi dengan sisi lain pertidaksamaan, tanda pertidaksamaannya harus dibalik.<\/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-88de95669c546ef6d18c28d0579fbe0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x<2\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"42\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Solusinya terdiri dari semua bilangan yang kurang dari 2. Oleh karena itu, domain definisi fungsi tersebut 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-505dcdf16c80fdf012163a8800d92836_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{Dom } \\ \\bm{f = (-\\infty,2) }\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, fungsi tersebut kontinu di setiap titik dalam domainnya.<\/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> Hitunglah kontinuitas fungsi 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-66e02ab966f87bc29b3791246fbf8032_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{4x-2}{\\sqrt{-2x-8}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"139\" style=\"vertical-align: -16px;\"><\/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\"> Pada penyebut pecahan kita mempunyai akar dengan indeks genap, sehingga fungsi tersebut akan ada setiap kali isi akar sama dengan atau lebih besar dari nol:<\/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-042efdf7af54fcbec527f0ee83e1b007_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x-8\\geq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Tapi juga, akarnya ada pada penyebut pecahan, dan penyebut pecahan tidak akan pernah sama dengan 0. Jadi fungsinya hanya akan ada jika isi akarnya lebih besar dari 0:<\/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-62002e9d71e0718d04d6d9db08d0e04b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x-8> 0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;95&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita selesaikan pertidaksamaan 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-336543c46271685f7d069786d2cf4e12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x>8&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;64&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/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-3e4a2af9f53dd0a356211660f770666e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x<\\cfrac{8}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"59\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ingatlah bahwa ketika kita mengubah sisi suatu bilangan negatif dengan mengalikan atau membagi suatu pertidaksamaan, kita juga harus memutar tanda pertidaksamaannya.<\/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-ee1c9c50b3c39064f9670f06f9bdc8fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x<-4\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"57\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Hasilnya semua angka kurang dari -4. Jadi domain dari fungsi tersebut, dan kontinuitasnya, ditentukan oleh interval 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-00cfb1cb63133c3092854bb810abfce8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{Dom } \\ \\bm{f = (-\\infty,-4) }\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" 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 8<\/h3>\n<p> Hitung nilai <em>k<\/em> agar fungsi tersebut kontinu sepanjang <\/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-6a134e3092861eafea1239dba23bea40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbb{R} .\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" 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-f7d8f0d6e0730c139c3baff0989a8fe7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left\\{ \\begin{array}{lcl} kx-1 &amp; \\text{si} &amp;  x \\leq 2 \\\\[2ex] 3x^2 - 5  &amp; \\text{si} &amp; x > 2 \\end{array} \\right.&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;65&#8243; width=&#8221;225&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/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\"> Agar fungsi tersebut kontinu, kedua batas lateral pada titik putus harus memberikan hasil yang sama. Oleh karena itu, pertama-tama kita menghitung batas lateral pada titik putus bagian yang tidak mempunyai <em>k<\/em> :<\/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-7eff7d699bc801340c66f4fd95c30b2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2^+} f(x) = \\lim_{x \\to 2} (3x^2 - 5) = 3\\cdot 2^2-5=\\bm{7}\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"324\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, agar fungsi sepotong-sepotong kontinu, batas sisi lainnya juga harus sama dengan 7.<\/p>\n<p class=\"has-text-align-left\"> Kami mencoba menghitung batas lateral lainnya:<\/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-1fc80cd47e7fd6cf50b2f2de57c4b40f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2^-} f(x) = \\lim_{x \\to 2} (kx-1) = k\\cdot2 -1= 2k-1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"350\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, agar suatu fungsi kontinu, dua batas lateral suatu titik harus memberikan hasil yang sama. Oleh karena itu, ekspresi yang diperoleh dari limit tersebut kita tetapkan sama dengan 7 (hasil dari limit lateral lainnya).<\/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-8b99f2f508e7c3f7ab4ebaa9f30638a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2k -1= 7\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir, kita selesaikan persamaan yang dihasilkan untuk mencari nilai <em>k<\/em> : <\/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-c591d3bbba83f012852966634d0d8234_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2k-1 = 7\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" 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-747038396badd9b1d5e6336cf463fe13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2k = 7 +1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" 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-fa5cd6bc10e8ce9c34542635d995323c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2k = 8\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" 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-1009397e0b35416230f2a5a3d307755a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k = \\cfrac{8}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"44\" 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-ffe7f00b80fc8f5c4961250446632d6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{k =4}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel kali ini kami akan menjelaskan apa itu fungsi kontinu dan cara menentukan kontinuitas suatu fungsi di suatu titik atau tidak. Selain itu, Anda akan menemukan properti fungsi kontinu dan analisis kontinuitas fungsi paling umum. Terakhir, Anda dapat berlatih dengan latihan yang diselesaikan pada fungsi kontinu untuk memahami konsep sepenuhnya. Apa yang dimaksud dengan &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/kontinuitas-fungsi-kontinuitas-suatu-fungsi\/\"> <span class=\"screen-reader-text\">Fungsi kontinu (kontinuitas suatu fungsi)<\/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":[43],"tags":[],"class_list":["post-24","post","type-post","status-publish","format-standard","hentry","category-batasan-fungsi"],"yoast_head":"<!-- This site is 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