{"id":10,"date":"2023-09-17T11:13:44","date_gmt":"2023-09-17T11:13:44","guid":{"rendered":"https:\/\/mathority.org\/id\/fungsi-eksponensial\/"},"modified":"2023-09-17T11:13:44","modified_gmt":"2023-09-17T11:13:44","slug":"fungsi-eksponensial","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/fungsi-eksponensial\/","title":{"rendered":"Fungsi eksponensial"},"content":{"rendered":"<p>Di halaman ini Anda akan mempelajari apa itu fungsi eksponensial dan juga cara merepresentasikan fungsi eksponensial pada grafik. Selain itu, Anda akan melihat semua karakteristiknya dan beberapa contoh untuk memahaminya sepenuhnya. Terakhir, Anda akan dapat berlatih dengan latihan dan soal yang diselesaikan selangkah demi selangkah tentang fungsi eksponensial. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-exponencial\"><\/span> Apa itu fungsi eksponensial?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Pengertian fungsi eksponensial adalah sebagai berikut: <\/p>\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;\">\n<p style=\"text-align:left\"> Dalam matematika, <strong>fungsi eksponensial<\/strong> adalah fungsi yang mempunyai variabel bebas <em>x<\/em> dalam pangkat. Dengan kata lain, mereka adalah 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-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<p style=\"text-align:left\"> Emas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah bilangan real positif dan berbeda dengan 1. <\/p>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-funciones-exponenciales\"><\/span> Contoh Fungsi Eksponensial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Fungsi berikut adalah contoh fungsi eksponensial: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf0f6145283a443b500a0bfebaec6ed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3^{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" 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-d2ca442ee75f74bd911dd3ab296ac873_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=4^{-x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" 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-b2052342e5fc234eb4428c63b727b4e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\left( \\frac{1}{2} \\right)^x\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"105\" 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-ef2b8e1b29b1b10d376713f6fa34fdfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=5^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-las-funciones-exponenciales\"><\/span> Karakteristik fungsi eksponensial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Fungsi eksponensial mempunyai sifat sebagai berikut:<\/p>\n<ul>\n<li> Domain fungsi eksponensial terdiri dari bilangan real, atau dengan kata lain fungsi eksponensial ada untuk nilai <em>x<\/em> apa pun.<\/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-91d461485d0f02bb14db6855a3774878_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f=\\mathbff{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul>\n<li> Namun fungsi tersebut hanya bernilai positif, sehingga rentang fungsi eksponensial terdiri dari bilangan real 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-36ed1f92f41441bd0c1d64faa0233a01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Im } f= (0,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Setiap fungsi eksponensial merupakan fungsi kontinu dan fungsi injektif.<\/li>\n<\/ul>\n<ul>\n<li> Jika fungsi tersebut tidak diterjemahkan, setiap fungsi eksponensial melewati titik (0,1). Karena fungsi yang dievaluasi ke nol selalu menghasilkan satu.<\/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-b49b6b1fa245db9037f372c69f2c1422_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0)=a^0=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Demikian pula, nilai fungsi eksponensial pada x=1 sama dengan basis.<\/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-c2f27dba606789a982e3e3c373bda0d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=a^1=a\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Jika basis kekuatan\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ab31067f7ffbb9fa0478bfb791f6295f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -5px;\"><\/p>\n<p> lebih besar dari 1, fungsi eksponensialnya meningkat. Sebaliknya jika koefisiennya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> berada pada interval antara 0 dan 1, fungsi eksponensialnya menurun.<\/li>\n<\/ul>\n<ul>\n<li> Secara umum sumbu x merupakan asimtot horizontal dari suatu fungsi eksponensial.<\/li>\n<\/ul>\n<ul>\n<li> Kebalikan dari fungsi eksponensial adalah fungsi logaritma. Oleh karena itu, grafik fungsi eksponensial dan fungsi logaritma adalah simetris terhadap garis y=x jika keduanya mempunyai basis yang sama. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-representar-en-una-grafica-una-funcion-exponencial\"><\/span> Cara Membuat Grafik Fungsi Eksponensial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Fungsi eksponensial sangat sederhana untuk direpresentasikan. Jadi mari kita lihat cara membuat grafik fungsi eksponensial pada grafik menggunakan sebuah contoh.<\/p>\n<ul>\n<li> Gambarkan fungsi eksponensial berikut pada grafik:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b460d8172e3f8e6633b62ab29e0f220_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam fungsi eksponensial, domain tidak perlu dihitung karena semuanya akan selalu berupa 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-0cd1539b66edeb38040ed80168e1fd9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, cukup dengan menyusun tabel nilai. Karena jenis fungsi ini banyak berubah dari satu titik ke titik lainnya, kita akan menghitung 5 poin. Namun semakin banyak poin yang kita hitung, representasi fungsinya akan semakin tepat. <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-201\">\n<div class=\"wp-block-column is-layout-flow\">\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e63b3712de818b714fafb781a7aed7b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)=2^0= 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-57601feaa5d5af3836989b041b20fd1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)=2^1= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c314f7ea92ec93e438d5ca2116be97fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)=2^2= 4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce96f914e1abc10b13488bc390af9501_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)=2^{-1}= 0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"253\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1526d8613884193ce46bf1d8515d8f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -2 \\ \\longrightarrow \\ f(-2)=2^{-2}= 0,25\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"262\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-299dcbadf5327b518849f641dd641f34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 0 &amp; 1 \\\\ 1 &amp; 2 \\\\ 2 &amp; 4 \\\\ -1 &amp; 0,5 \\\\ -2 &amp; 0,25 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"90\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Kami merekomendasikan penggunaan kalkulator untuk mencari poin dalam tabel nilai, karena rumit untuk dihitung dengan tangan.<\/p>\n<p> Sekarang kita mewakili titik-titik pada grafik <strong>:<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/cropped-polynomials-icon-1.png.png\" alt=\"\" class=\"wp-image-249\" width=\"274\" height=\"329\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Dan terakhir, kami menggabungkan titik-titik tersebut dan memperluas fungsinya: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-representation-graphique-d-une-fonction-exponentielle.webp\" alt=\"cara merepresentasikan atau membuat grafik fungsi eksponensial\" class=\"wp-image-250\" width=\"274\" height=\"326\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Perhatikan bahwa fungsi di sebelah kanan terus bertambah hingga tak terhingga.<\/p>\n<p> Sebaliknya, fungsi di sebelah kiri berkurang tetapi tidak pernah mencapai 0. Meskipun sangat dekat dengannya, namun tidak pernah menyentuhnya. Artinya garis y=0 (sumbu x) merupakan asimtot mendatar. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-funciones-exponenciales\"><\/span> Latihan soal fungsi eksponensial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Gambarkan fungsi eksponensial 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-03ffe9b15e527e77fc38e7a090b9086d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= 2^x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" 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 eksponensial, jadi untuk merepresentasikannya Anda harus membuat tabel nilai yang memberikan nilai pada variabel x: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-204\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c782f0c5fc2c9576431a0653e6e954da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)= 2^0+1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"228\" 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-1a2424217eb051ccbc60bd9c9832cb16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)= 2^1+1=3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"229\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-46a35a2a78981d594a4599130a5128ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)= 2^2+1=5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"228\" 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-fceb9d30fc89075d6f6d367db21aefa0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)= 2^{-1}+1=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"283\" 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-d1d391b6991faa22024aa6164e79fde1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -2 \\ \\longrightarrow \\ f(-2)= 2^{-2}+1=1,25\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"292\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5623433725def7676c75afcfdf23ad6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 0 &amp; 2 \\\\ 1 &amp; 3 \\\\ 2 &amp; 5 \\\\ -1 &amp; 1,5 \\\\ -2 &amp; 1,25 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"90\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Setelah kita memiliki tabel nilainya, kita memplot titik-titik yang diperoleh pada grafik dan memplot fungsinya: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-etape-par-etape-des-fonctions-exponentielles.webp\" alt=\"latihan diselesaikan langkah demi langkah fungsi eksponensial\" class=\"wp-image-251\" width=\"301\" height=\"298\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> Perhatikan bahwa fungsi di sebelah kanan terus bertambah hingga tak terhingga. Sebaliknya, di sebelah kiri, fungsinya berkurang tetapi tidak pernah melebihi 1. Memang benar, fungsi tersebut mempunyai asimtot horizontal di sebelah kanan y=1.<\/p>\n<p class=\"has-text-align-left\"> Dalam hal ini, asimtot horizontal berada di y=1 dan bukan pada sumbu OX karena translasi vertikal satu satuan ke atas telah dilakukan menuju fungsi tersebut.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 2<\/h3>\n<p> Gambarkan fungsi eksponensial 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-b9a894948fd1963ec5090a0e42d82da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left(\\frac{1}{3}\\right)^x\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"105\" style=\"vertical-align: -17px;\"><\/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 eksponensial, jadi untuk merepresentasikannya secara grafis Anda harus membuat tabel nilai yang memberikan nilai pada variabel x: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-207\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1ce9dea9f80eeafd40e7e6e13b200ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)= \\left(\\cfrac{1}{3}\\right)^0 = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"228\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-093a357ac3d5530f00f1f69ccd5a0ef4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)= \\left(\\cfrac{1}{3}\\right)^1 = 0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"255\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0c324f0d99a2076cc1bfb2d38acb9b76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)= \\left(\\cfrac{1}{3}\\right)^2 = 0,11\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"254\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e55ea725b4125b1f53dce7b5b42ea633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)= \\left(\\cfrac{1}{3}\\right)^{-1} = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"267\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7f1abd0ebf23e5d165e5d1cfd94afb4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -2 \\ \\longrightarrow \\ f(-2)= \\left(\\cfrac{1}{3}\\right)^{-2} = 9\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"267\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cbf76eff59299da8ebaf3185eef2c654_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 0 &amp; 1 \\\\ 1 &amp; 0,33 \\\\ 2 &amp; 0,11 \\\\ -1 &amp; 3 \\\\ -2 &amp; 9 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"90\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Setelah kita memiliki tabel nilainya, kita memplot titik-titik yang dihitung pada grafik dan menggambar fungsinya: <\/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\/polynomes-px.png\" alt=\"menyelesaikan latihan fungsi eksponensial\" class=\"wp-image-252\" width=\"266\" height=\"454\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> Perhatikan bahwa fungsi di sebelah kiri terus bertambah hingga tak terbatas. Di sisi lain, di sebelah kanan, fungsinya berkurang tetapi tidak pernah melebihi 0. Memang benar, fungsi tersebut memiliki asimtot horizontal di y=0 (sumbu X).<\/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 eksponensial 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-6abae87b33d734a0f0df3fda4b4af143_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left(\\frac{1}{2}\\right)^x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"136\" style=\"vertical-align: -17px;\"><\/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 eksponensial, jadi untuk menggambarnya Anda harus membuat tabel nilai yang mengevaluasi fungsi tersebut di beberapa titik: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-210\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d86d4d4bb01fc8784c0e389848e82c3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)= \\left(\\cfrac{1}{2}\\right)^0+3 = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"259\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa71d27c766686ff32712a8b1767e1ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)= \\left(\\cfrac{1}{2}\\right)^1+3 = 3,5\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"275\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-86b1fa3f8b4652a02cc02efc2a75bd80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)= \\left(\\cfrac{1}{2}\\right)^2+3 = 3,25\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"284\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c27100fdc0eb9ede26c4704ed45d8914_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)= \\left(\\cfrac{1}{2}\\right)^{-1}+3 = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"297\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7389ec7cd9ac887cb79f083ba84e92e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -2 \\ \\longrightarrow \\ f(-2)= \\left(\\cfrac{1}{2}\\right)^{-2}+3 = 7\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"298\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2d6c182e2785f23f50b3b16e4e183157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 0 &amp; 4 \\\\ 1 &amp; 3,5 \\\\ 2 &amp; 3,25 \\\\ -1 &amp; 5 \\\\ -2 &amp; 7 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"90\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Terakhir, kami merepresentasikan titik-titik yang diperoleh pada grafik dan memplot fungsinya: <\/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\/cropped-polynomes-px.png.png\" alt=\"masalah fungsi eksponensial\" class=\"wp-image-253\" width=\"305\" height=\"372\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> Perhatikan bahwa fungsi di sebelah kiri bertambah tanpa batas hingga tak terbatas. Sebaliknya, di sebelah kanan, fungsinya berkurang tetapi tidak pernah melebihi 3. Memang benar, fungsi tersebut mempunyai asimtot horizontal di y=3.<\/p>\n<p class=\"has-text-align-left\"> Dalam hal ini, asimtot horizontal berada di y=3 dan bukan di sumbu X karena fungsinya telah dipindahkan secara vertikal tiga satuan ke atas.<\/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> Selesaikan soal berikut mengenai fungsi eksponensial.<\/p>\n<ul>\n<li> Tentukan nilai dari\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> sehingga fungsi eksponensial selanjutnya melalui titik (2.8). <\/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-be030f5f0ee0aada1e1c389763b331d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=k\\cdot 2^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"98\" 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\"> Fungsi tersebut harus melalui titik (2,8), sehingga kita dapat mensubstitusikan nilai <em>x<\/em> dan <em>f(x)<\/em> titik tersebut ke dalam fungsi tersebut untuk mencari nilai konstanta <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-bb3d3396e39826e0d6223a79bafe6bf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=k\\cdot 2^x \\ \\xrightarrow{x \\ = \\ 2 \\ ; \\ f(x) \\ = \\ 8} \\ 8 = k \\cdot 2^2\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"310\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan sekarang 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-a345fdf8c61dc26e5092176b51a29e59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8 = k \\cdot 2^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" 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-e4683f83c268d651c548b98d2320441b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8 = k \\cdot 4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" 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-d793900a9bfa50bf89f48216a403e616_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{8}{4} = k\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"41\" 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-34ed53fa864ab9ac888742f196a6453c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{ 2 = k}\" 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<h3 class=\"wp-block-heading\">Latihan 5<\/h3>\n<p> Selesaikan soal berikut mengenai fungsi eksponensial.<\/p>\n<p> Populasi rayap berkembang biak menurut 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-1b41270bdb73979966e8c8e118e76cf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(t)=3^{t+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Emas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59d54ba73238a26eb8acae54cb83607e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(t)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"30\" style=\"vertical-align: -5px;\"><\/p>\n<p> adalah jumlah rayap dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> waktu telah berlalu dalam beberapa bulan.<\/p>\n<p> Berapa jumlah rayap setelah 1 tahun? <\/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 menghitung jumlah rayap dalam setahun, cukup masukkan waktu yang telah berlalu (1 tahun) ke dalam fungsi tersebut. Namun karena fungsi <em>t<\/em> adalah bulan yang telah berlalu dan bukan tahun, maka kita harus memasukkan <em>t<\/em> =12 karena dalam satu tahun terdapat 12 bulan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1b41270bdb73979966e8c8e118e76cf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(t)=3^{t+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"85\" 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-68f69b244c701ac9238c9939e5d85791_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(12)=3^{12+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-406c5d11e786f4624ffc7834f6b8fe8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(12)=3^{13}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"89\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menyelesaikannya dengan kalkulator:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b44ece2cfd87c845152ec5aa481188fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(12)= 1594323\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi setelah satu tahun akan ada 1.594.323 rayap.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan mempelajari apa itu fungsi eksponensial dan juga cara merepresentasikan fungsi eksponensial pada grafik. Selain itu, Anda akan melihat semua karakteristiknya dan beberapa contoh untuk memahaminya sepenuhnya. Terakhir, Anda akan dapat berlatih dengan latihan dan soal yang diselesaikan selangkah demi selangkah tentang fungsi eksponensial. Apa itu fungsi eksponensial? Pengertian fungsi eksponensial &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/fungsi-eksponensial\/\"> <span class=\"screen-reader-text\">Fungsi eksponensial<\/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-10","post","type-post","status-publish","format-standard","hentry","category-representasi-fungsi"],"yoast_head":"<!-- This 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