{"id":13,"date":"2023-09-17T11:13:44","date_gmt":"2023-09-17T11:13:44","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%88%d8%b8%d9%8a%d9%81%d8%a9-%d8%a7%d9%84%d8%a3%d8%b3%d9%8a%d8%a9\/"},"modified":"2023-09-17T11:13:44","modified_gmt":"2023-09-17T11:13:44","slug":"%d9%88%d8%b8%d9%8a%d9%81%d8%a9-%d8%a7%d9%84%d8%a3%d8%b3%d9%8a%d8%a9","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%88%d8%b8%d9%8a%d9%81%d8%a9-%d8%a7%d9%84%d8%a3%d8%b3%d9%8a%d8%a9\/","title":{"rendered":"\u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0633\u0648\u0641 \u062a\u0643\u062a\u0634\u0641 \u0645\u0627 \u0647\u064a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0633\u064a\u0629 \u0648\u0643\u0630\u0644\u0643 \u0643\u064a\u0641\u064a\u0629 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0639\u0644\u0649 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u0631\u0649 \u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635\u0647 \u0648\u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0644\u0641\u0647\u0645\u0647 \u0628\u0627\u0644\u0643\u0627\u0645\u0644. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0633\u0648\u0641 \u062a\u0643\u0648\u0646 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0648\u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0639\u0644\u0649 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0633\u064a\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-exponencial\"><\/span> \u0645\u0627 \u0647\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a: <\/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;;text-align:right;direction:rtl\">\n<p style=\"text-align:left;text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c <strong>\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0633\u064a\u0629<\/strong> \u0647\u064a \u062f\u0648\u0627\u0644 \u0644\u0647\u0627 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0645\u0633\u062a\u0642\u0644 <em>x<\/em> \u0641\u064a \u0623\u0633 \u0627\u0644\u0642\u0648\u0629. \u0648\u0628\u0639\u0628\u0627\u0631\u0629 \u0623\u062e\u0631\u0649 \u0641\u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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;text-align:right;direction:rtl\"> \u0630\u0647\u0628<\/p>\n<p style=\";text-align:right;direction:rtl\">\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> \u0647\u0648 \u0639\u062f\u062f \u062d\u0642\u064a\u0642\u064a \u0645\u0648\u062c\u0628 \u0648\u064a\u062e\u062a\u0644\u0641 \u0639\u0646 1. <\/p>\n<\/div>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplos-de-funciones-exponenciales\"><\/span> \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0627\u0644\u0623\u0633\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0647\u064a \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0627\u0644\u0623\u0633\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-las-funciones-exponenciales\"><\/span> \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0633\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0633\u064a\u0629 \u0644\u0647\u0627 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0645\u062c\u0627\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u064a\u062a\u0643\u0648\u0646 \u0645\u0646 \u0623\u0631\u0642\u0627\u0645 \u062d\u0642\u064a\u0642\u064a\u0629\u060c \u0623\u0648 \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u062a\u0648\u062c\u062f \u062f\u0627\u0644\u0629 \u0623\u0633\u064a\u0629 \u0644\u0623\u064a \u0642\u064a\u0645\u0629 \u0644\u0640 <em>x<\/em> .<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u062a\u0623\u062e\u0630 \u0642\u064a\u0645\u064b\u0627 \u0645\u0648\u062c\u0628\u0629 \u0641\u0642\u0637\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0646\u0637\u0627\u0642 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u064a\u062a\u0643\u0648\u0646 \u0645\u0646 \u0623\u0631\u0642\u0627\u0645 \u062d\u0642\u064a\u0642\u064a\u0629 \u0645\u0648\u062c\u0628\u0629.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0643\u0644 \u062f\u0627\u0644\u0629 \u0623\u0633\u064a\u0629 \u0647\u064a \u062f\u0627\u0644\u0629 \u0645\u0633\u062a\u0645\u0631\u0629 \u0648\u062d\u0642\u0646\u064a\u0629.<\/li>\n<\/ul>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0627 \u0644\u0645 \u062a\u062a\u0645 \u062a\u0631\u062c\u0645\u0629 \u0627\u0644\u062f\u0627\u0644\u0629\u060c \u0641\u0625\u0646 \u0623\u064a \u062f\u0627\u0644\u0629 \u0623\u0633\u064a\u0629 \u062a\u0645\u0631 \u0639\u0628\u0631 \u0627\u0644\u0646\u0642\u0637\u0629 (0\u060c1). \u0644\u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u064a \u0642\u064a\u0645\u062a\u0647\u0627 \u0635\u0641\u0631 \u062a\u0639\u0637\u064a \u062f\u0627\u0626\u0645\u064b\u0627 \u0648\u0627\u062d\u062f\u064b\u0627.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u0645\u062b\u0644\u060c \u0641\u0625\u0646 \u0642\u064a\u0645\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0639\u0646\u062f x=1 \u062a\u0633\u0627\u0648\u064a \u0627\u0644\u0623\u0633\u0627\u0633.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0633\u0644\u0637\u0629\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> \u0623\u0643\u0628\u0631 \u0645\u0646 1\u060c \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0622\u062e\u0630\u0629 \u0641\u064a \u0627\u0644\u062a\u0632\u0627\u064a\u062f. \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u0639\u0627\u0645\u0644<\/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> \u0641\u064a \u0627\u0644\u0641\u062a\u0631\u0629 \u0628\u064a\u0646 0 \u0648 1\u060c \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0622\u062e\u0630\u0629 \u0641\u064a \u0627\u0644\u062a\u0646\u0627\u0642\u0635.<\/li>\n<\/ul>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0628\u0634\u0643\u0644 \u0639\u0627\u0645\u060c \u0627\u0644\u0645\u062d\u0648\u0631 \u0627\u0644\u0633\u064a\u0646\u064a \u0647\u0648 \u062e\u0637 \u0645\u0642\u0627\u0631\u0628 \u0623\u0641\u0642\u064a \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629.<\/li>\n<\/ul>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0645\u0639\u0643\u0648\u0633 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0647\u0648 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u064a\u0629. \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0631\u0633\u0648\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0648\u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u064a\u0629 \u062a\u0643\u0648\u0646 \u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u062d\u0648\u0644 \u0627\u0644\u062e\u0637 y=x \u0625\u0630\u0627 \u0643\u0627\u0646 \u0643\u0644\u0627\u0647\u0645\u0627 \u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0623\u0633\u0627\u0633. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"como-representar-en-una-grafica-una-funcion-exponencial\"><\/span> \u0643\u064a\u0641\u064a\u0629 \u0631\u0633\u0645 \u062f\u0627\u0644\u0629 \u0623\u0633\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0627\u0644\u0633\u0647\u0644 \u062c\u062f\u064b\u0627 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0627\u0644\u0623\u0633\u064a\u0629. \u0644\u0630\u0644\u0643 \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0643\u064a\u0641\u064a\u0629 \u0631\u0633\u0645 \u062f\u0627\u0644\u0629 \u0623\u0633\u064a\u0629 \u0639\u0644\u0649 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062b\u0627\u0644.<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0627\u0631\u0633\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0639\u0644\u0649 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0633\u064a\u0629\u060c \u0644\u064a\u0633\u062a \u0647\u0646\u0627\u0643 \u062d\u0627\u062c\u0629 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062c\u0627\u0644\u060c \u0644\u0623\u0646\u0647\u0627 \u0633\u062a\u0643\u0648\u0646 \u062f\u0627\u0626\u0645\u064b\u0627 \u0623\u0631\u0642\u0627\u0645\u064b\u0627 \u062d\u0642\u064a\u0642\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643 \u064a\u0643\u0641\u064a \u0625\u0639\u062f\u0627\u062f \u062c\u062f\u0648\u0644 \u0627\u0644\u0642\u064a\u0645. \u0648\u0628\u0645\u0627 \u0623\u0646 \u0647\u0630\u0647 \u0627\u0644\u0623\u0646\u0648\u0627\u0639 \u0645\u0646 \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u062a\u062a\u063a\u064a\u0631 \u0643\u062b\u064a\u0631\u064b\u0627 \u0645\u0646 \u0646\u0642\u0637\u0629 \u0625\u0644\u0649 \u0623\u062e\u0631\u0649\u060c \u0641\u0633\u0648\u0641 \u0646\u0642\u0648\u0645 \u0628\u062d\u0633\u0627\u0628 5 \u0646\u0642\u0627\u0637. \u0644\u0643\u0646 \u0643\u0644\u0645\u0627 \u0632\u0627\u062f \u0639\u062f\u062f \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062a\u064a \u0646\u062d\u0633\u0628\u0647\u0627\u060c \u0623\u0635\u0628\u062d \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0623\u0643\u062b\u0631 \u062f\u0642\u0629. <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-201\" style=\";text-align:right;direction:rtl\">\n<div class=\"wp-block-column is-layout-flow\" style=\";text-align:right;direction:rtl\">\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\">\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0646\u0646\u0635\u062d \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629 \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0646\u0642\u0627\u0637 \u0641\u064a \u062c\u062f\u0648\u0644 \u0627\u0644\u0642\u064a\u0645\u060c \u0646\u0638\u0631\u064b\u0627 \u0644\u0635\u0639\u0648\u0628\u0629 \u062d\u0633\u0627\u0628\u0647\u0627 \u064a\u062f\u0648\u064a\u064b\u0627.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0646\u0645\u062b\u0644 \u0627\u0644\u0646\u0642\u0627\u0637 \u0639\u0644\u0649 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a <strong>:<\/strong> <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0642\u0648\u0645 \u0628\u0631\u0628\u0637 \u0627\u0644\u0646\u0642\u0627\u0637 \u0648\u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u062f\u0627\u0644\u0629: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\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=\"\u0643\u064a\u0641\u064a\u0629 \u062a\u0645\u062b\u064a\u0644 \u0623\u0648 \u0631\u0633\u0645 \u0628\u064a\u0627\u0646\u064a \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629\" class=\"wp-image-250\" width=\"274\" height=\"326\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0627\u062d\u0638 \u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0639\u0644\u0649 \u0627\u0644\u064a\u0645\u064a\u0646 \u062a\u0633\u062a\u0645\u0631 \u0641\u064a \u0627\u0644\u0646\u0645\u0648 \u062d\u062a\u0649 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u060c \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0639\u0644\u0649 \u0627\u0644\u064a\u0633\u0627\u0631 \u062a\u062a\u0646\u0627\u0642\u0635 \u0648\u0644\u0643\u0646\u0647\u0627 \u0644\u0627 \u062a\u0635\u0644 \u0623\u0628\u062f\u064b\u0627 \u0625\u0644\u0649 0. \u0648\u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646\u0647\u0627 \u062a\u0642\u062a\u0631\u0628 \u0645\u0646\u0647\u0627 \u0643\u062b\u064a\u0631\u064b\u0627\u060c \u0625\u0644\u0627 \u0623\u0646\u0647\u0627 \u0644\u0627 \u062a\u0644\u0645\u0633\u0647\u0627 \u0623\u0628\u062f\u064b\u0627. \u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646 \u0627\u0644\u062e\u0637 y=0 (\u0627\u0644\u0645\u062d\u0648\u0631 x) \u0647\u0648 \u062e\u0637 \u0645\u0642\u0627\u0631\u0628 \u0623\u0641\u0642\u064a. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-funciones-exponenciales\"><\/span> \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0633\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 1<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0631\u0633\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0625\u0646\u0647\u0627 \u062f\u0627\u0644\u0629 \u0623\u0633\u064a\u0629\u060c \u0644\u0630\u0627 \u0644\u062a\u0645\u062b\u064a\u0644\u0647\u0627 \u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u0625\u0646\u0634\u0627\u0621 \u062c\u062f\u0648\u0644 \u0642\u064a\u0645 \u064a\u0639\u0637\u064a \u0642\u064a\u0645 \u0644\u0644\u0645\u062a\u063a\u064a\u0631 x: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-204\" style=\";text-align:right;direction:rtl\">\n<div class=\"wp-block-column is-layout-flow\" style=\";text-align:right;direction:rtl\">\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\">\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u062d\u0635\u0648\u0644\u0646\u0627 \u0639\u0644\u0649 \u062c\u062f\u0648\u0644 \u0627\u0644\u0642\u064a\u0645\u060c \u0646\u0631\u0633\u0645 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0648\u0646\u0631\u0633\u0645 \u0627\u0644\u062f\u0627\u0644\u0629: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\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=\"\u062a\u0645\u0631\u064a\u0646 \u062a\u0645 \u062d\u0644\u0647 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0633\u064a\u0629\" class=\"wp-image-251\" width=\"301\" height=\"298\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0627\u062d\u0638 \u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0639\u0644\u0649 \u0627\u0644\u064a\u0645\u064a\u0646 \u062a\u0633\u062a\u0645\u0631 \u0641\u064a \u0627\u0644\u0646\u0645\u0648 \u062d\u062a\u0649 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629. \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0639\u0644\u0649 \u0627\u0644\u064a\u0633\u0627\u0631\u060c \u062a\u0642\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0648\u0644\u0643\u0646\u0647\u0627 \u0644\u0627 \u062a\u062a\u062c\u0627\u0648\u0632 1 \u0623\u0628\u062f\u064b\u0627. \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u062e\u0637 \u062a\u0642\u0627\u0631\u0628 \u0623\u0641\u0642\u064a \u0639\u0644\u0649 \u0627\u0644\u064a\u0645\u064a\u0646 y=1.<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u064a\u0643\u0648\u0646 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0642\u0627\u0631\u0628 \u0627\u0644\u0623\u0641\u0642\u064a \u0639\u0646\u062f y=1 \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0627\u0644\u0645\u062d\u0648\u0631 OX \u0644\u0623\u0646\u0647 \u062a\u0645 \u0625\u062c\u0631\u0627\u0621 \u062a\u0631\u062c\u0645\u0629 \u0631\u0623\u0633\u064a\u0629 \u0644\u0648\u062d\u062f\u0629 \u0648\u0627\u062d\u062f\u0629 \u0644\u0623\u0639\u0644\u0649 \u0628\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u062f\u0627\u0644\u0629.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u062a\u0645\u0631\u064a\u0646 2<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0631\u0633\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0639\u0644\u0649 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0625\u0646\u0647\u0627 \u062f\u0627\u0644\u0629 \u0623\u0633\u064a\u0629\u060c \u0644\u0630\u0627 \u0644\u062a\u0645\u062b\u064a\u0644\u0647\u0627 \u0628\u064a\u0627\u0646\u064a\u0627\u064b \u064a\u062c\u0628 \u0625\u0646\u0634\u0627\u0621 \u062c\u062f\u0648\u0644 \u0642\u064a\u0645 \u064a\u0639\u0637\u064a \u0642\u064a\u0645\u0627\u064b \u0644\u0644\u0645\u062a\u063a\u064a\u0631 x: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-207\" style=\";text-align:right;direction:rtl\">\n<div class=\"wp-block-column is-layout-flow\" style=\";text-align:right;direction:rtl\">\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\">\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u062d\u0635\u0648\u0644\u0646\u0627 \u0639\u0644\u0649 \u062c\u062f\u0648\u0644 \u0627\u0644\u0642\u064a\u0645\u060c \u0646\u0631\u0633\u0645 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u0645\u062d\u0633\u0648\u0628\u0629 \u0639\u0644\u0649 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0648\u0646\u0631\u0633\u0645 \u0627\u0644\u062f\u0627\u0644\u0629: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\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=\"\u062d\u0644 \u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0633\u064a\u0629\" class=\"wp-image-252\" width=\"266\" height=\"454\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0627\u062d\u0638 \u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0639\u0644\u0649 \u0627\u0644\u064a\u0633\u0627\u0631 \u062a\u0633\u062a\u0645\u0631 \u0641\u064a \u0627\u0644\u0646\u0645\u0648 \u062d\u062a\u0649 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629. \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0639\u0644\u0649 \u0627\u0644\u064a\u0645\u064a\u0646\u060c \u062a\u0642\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0648\u0644\u0643\u0646\u0647\u0627 \u0644\u0627 \u062a\u062a\u062c\u0627\u0648\u0632 0 \u0623\u0628\u062f\u064b\u0627. \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u062e\u0637 \u062a\u0642\u0627\u0631\u0628 \u0623\u0641\u0642\u064a \u0639\u0646\u062f y=0 (\u0627\u0644\u0645\u062d\u0648\u0631 X).<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 3<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0631\u0633\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0639\u0644\u0649 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0625\u0646\u0647\u0627 \u062f\u0627\u0644\u0629 \u0623\u0633\u064a\u0629\u060c \u0644\u0630\u0627 \u0644\u0631\u0633\u0645\u0647\u0627 \u064a\u062c\u0628 \u0625\u0646\u0634\u0627\u0621 \u062c\u062f\u0648\u0644 \u0642\u064a\u0645 \u064a\u0642\u064a\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u0641\u064a \u0639\u062f\u0629 \u0646\u0642\u0627\u0637: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-210\" style=\";text-align:right;direction:rtl\">\n<div class=\"wp-block-column is-layout-flow\" style=\";text-align:right;direction:rtl\">\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\">\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0645\u062b\u0644 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0648\u0646\u0631\u0633\u0645 \u0627\u0644\u062f\u0627\u0644\u0629: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\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=\"\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629\" class=\"wp-image-253\" width=\"305\" height=\"372\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0627\u062d\u0638 \u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0639\u0644\u0649 \u0627\u0644\u064a\u0633\u0627\u0631 \u062a\u0646\u0645\u0648 \u0628\u0634\u0643\u0644 \u063a\u064a\u0631 \u0645\u062d\u062f\u0648\u062f \u0625\u0644\u0649 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629. \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0639\u0644\u0649 \u0627\u0644\u064a\u0645\u064a\u0646\u060c \u062a\u0642\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0648\u0644\u0643\u0646\u0647\u0627 \u0644\u0627 \u062a\u062a\u062c\u0627\u0648\u0632 3 \u0623\u0628\u062f\u064b\u0627. \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u062e\u0637 \u062a\u0642\u0627\u0631\u0628 \u0623\u0641\u0642\u064a \u0639\u0646\u062f y=3.<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u064a\u0643\u0648\u0646 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0642\u0627\u0631\u0628 \u0627\u0644\u0623\u0641\u0642\u064a \u0639\u0646\u062f y=3 \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0627\u0644\u0645\u062d\u0648\u0631 X \u0644\u0623\u0646\u0647 \u062a\u0645 \u0646\u0642\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0631\u0623\u0633\u064a\u064b\u0627 \u062b\u0644\u0627\u062b \u0648\u062d\u062f\u0627\u062a \u0644\u0623\u0639\u0644\u0649.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 4<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0644 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0641\u064a\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0627\u0644\u0623\u0633\u064a\u0629.<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u062a\u062d\u062f\u064a\u062f \u0642\u064a\u0645\u0629\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> \u0628\u062d\u064a\u062b \u062a\u0645\u0631 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u0627\u0644\u0646\u0642\u0637\u0629 (2.8). <\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\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;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u064a\u062c\u0628 \u0623\u0646 \u062a\u0645\u0631 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0627\u0644\u0646\u0642\u0637\u0629 (2,8)\u060c \u062d\u062a\u0649 \u0646\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0642\u064a\u0645 <em>x<\/em> \u0648 <em>f(x)<\/em> \u0644\u0644\u0646\u0642\u0637\u0629 \u0641\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0625\u064a\u062c\u0627\u062f \u0642\u064a\u0645\u0629 \u0627\u0644\u062b\u0627\u0628\u062a <em>k:<\/em><\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0648\u0627\u0644\u0622\u0646 \u0646\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0646\u0627\u062a\u062c\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 5<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0644 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0641\u064a\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0627\u0644\u0623\u0633\u064a\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u062a\u0643\u0627\u062b\u0631 \u062c\u0645\u0627\u0639\u0629 \u0627\u0644\u0646\u0645\u0644 \u0627\u0644\u0623\u0628\u064a\u0636 \u0648\u0641\u0642\u0627\u064b \u0644\u0644\u0648\u0638\u064a\u0641\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0630\u0647\u0628<\/p>\n<p style=\";text-align:right;direction:rtl\">\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> \u0647\u0648 \u0639\u062f\u062f \u0627\u0644\u0646\u0645\u0644 \u0627\u0644\u0623\u0628\u064a\u0636 \u0648<\/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> \u0644\u0642\u062f \u0645\u0631 \u0627\u0644\u0648\u0642\u062a \u0645\u0646\u0630 \u0623\u0634\u0647\u0631.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645 \u0639\u062f\u062f \u0627\u0644\u0646\u0645\u0644 \u0627\u0644\u0623\u0628\u064a\u0636 \u0633\u064a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u0628\u0639\u062f \u0633\u0646\u0629 \u0648\u0627\u062d\u062f\u0629\u061f <\/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;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u062d\u0633\u0627\u0628 \u0639\u062f\u062f \u0627\u0644\u0646\u0645\u0644 \u0627\u0644\u0623\u0628\u064a\u0636 \u0627\u0644\u0630\u064a \u0633\u064a\u0643\u0648\u0646 \u0645\u0648\u062c\u0648\u062f\u064b\u0627 \u062e\u0644\u0627\u0644 \u0639\u0627\u0645\u060c \u0645\u0627 \u0639\u0644\u064a\u0643 \u0633\u0648\u0649 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u0648\u0642\u062a \u0627\u0644\u0645\u0646\u0642\u0636\u064a (\u0633\u0646\u0629 \u0648\u0627\u062d\u062f\u0629) \u0641\u064a \u0627\u0644\u062f\u0627\u0644\u0629. \u0648\u0644\u0643\u0646 \u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 <em>t<\/em> \u0647\u064a \u0627\u0644\u0623\u0634\u0647\u0631 \u0627\u0644\u0645\u0646\u0642\u0636\u064a\u0629 \u0648\u0644\u064a\u0633 \u0627\u0644\u0633\u0646\u0648\u0627\u062a\u060c \u0641\u064a\u062c\u0628 \u0623\u0646 \u0646\u0636\u0639 <em>t<\/em> = 12 \u062d\u064a\u062b \u064a\u0648\u062c\u062f \u0641\u064a \u0627\u0644\u0633\u0646\u0629 12 \u0634\u0647\u0631\u064b\u0627: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0644 \u0628\u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0646 \u0628\u0639\u062f \u0639\u0627\u0645 \u0648\u0627\u062d\u062f \u0633\u064a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 1,594,323 \u0646\u0645\u0644\u064b\u0627 \u0623\u0628\u064a\u0636\u064b\u0627.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0633\u0648\u0641 \u062a\u0643\u062a\u0634\u0641 \u0645\u0627 \u0647\u064a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0633\u064a\u0629 \u0648\u0643\u0630\u0644\u0643 \u0643\u064a\u0641\u064a\u0629 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0639\u0644\u0649 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u0631\u0649 \u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635\u0647 \u0648\u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0644\u0641\u0647\u0645\u0647 \u0628\u0627\u0644\u0643\u0627\u0645\u0644. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0633\u0648\u0641 \u062a\u0643\u0648\u0646 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0648\u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0639\u0644\u0649 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0633\u064a\u0629. \u0645\u0627 \u0647\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629\u061f \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a: &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d9%88%d8%b8%d9%8a%d9%81%d8%a9-%d8%a7%d9%84%d8%a3%d8%b3%d9%8a%d8%a9\/\"> <span class=\"screen-reader-text\">\u0627\u0644\u062f\u0627\u0644\u0629 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