{"id":153606,"date":"2022-03-25T22:36:39","date_gmt":"2022-03-25T17:06:39","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/increasing-and-decreasing-functions-and-monotonicity\/"},"modified":"2022-12-31T17:48:18","modified_gmt":"2022-12-31T12:18:18","slug":"increasing-and-decreasing-functions-and-monotonicity","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/","title":{"rendered":"Increasing And Decreasing Functions And Monotonicity"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/#An_Introduction\" title=\"An Introduction\">An Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/#Increasing_Decreasing_Functions\" title=\"Increasing Decreasing Functions\">Increasing Decreasing Functions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/#Increasing_Function_Definition\" title=\"Increasing Function Definition\">Increasing Function Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/#Decreasing_Function_Definition\" title=\"Decreasing Function Definition\">Decreasing Function Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/#Monotonic_Functions\" title=\"Monotonic Functions\">Monotonic Functions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/#Increasing_and_Decreasing_Functions_Examples\" title=\"Increasing and Decreasing Functions Examples\">Increasing and Decreasing Functions Examples<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/#Monotonically_Increasing_Functions\" title=\"Monotonically Increasing Functions\">Monotonically Increasing Functions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/#Monotonically_Increasing_Function_Example\" title=\"Monotonically Increasing Function Example\">Monotonically Increasing Function Example<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/#Monotonically_Decreasing_Function\" title=\"Monotonically Decreasing Function\">Monotonically Decreasing Function<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/#Monotonically_Decreasing_Function_Example\" title=\"Monotonically Decreasing Function Example\">Monotonically Decreasing Function Example<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/#Tips_to_Study_Increasing_and_Decreasing_Functions_and_Monotonicity\" title=\"Tips to Study Increasing and Decreasing Functions and Monotonicity\">Tips to Study Increasing and Decreasing Functions and Monotonicity<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"An_Introduction\"><\/span>An Introduction<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>to the Internet of Things<\/p>\n<p>The internet of things (IoT) is a term for the ever-growing network of physical objects and devices that are connected to the internet. These objects can communicate with each other and exchange data, and they often use sensors to interact with their surroundings.<\/p>\n<p>The potential applications for the IoT are endless, and it&#8217;s already being used in a variety of ways. For example, hospitals are using the IoT to monitor patients&#8217; vital signs, and cities are using it to manage traffic and energy consumption.<\/p>\n<p>The IoT is still in its early stages, and it&#8217;s evolving rapidly. As more devices are connected to the internet, the potential for new applications and use cases continues to grow.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-153605 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/increasing-and-decreasing-functions-and-monotonicity.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/increasing-and-decreasing-functions-and-monotonicity.jpg?v=1648227994 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/increasing-and-decreasing-functions-and-monotonicity-300x212.jpg?v=1648227994 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Increasing_Decreasing_Functions\"><\/span>Increasing Decreasing Functions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An increasing function is a mathematical function in which each output value is greater than the output value of the function before it. A decreasing function is a mathematical function in which each output value is less than the output value of the function before it.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Increasing_Function_Definition\"><\/span>Increasing Function Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The purpose of an increasing function is to increase the value of a particular variable by a specific amount. The function will take in an input value and will return an output value that is greater than the input value. The function can be used to increase the value of a number, a text string, or a file size.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Decreasing_Function_Definition\"><\/span>Decreasing Function Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A decreasing function is a function in which the output decreases as the input increases.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Monotonic_Functions\"><\/span>Monotonic Functions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A monotonic function is a function that either increases or decreases without reversing direction. In other words, a monotonic function is either always increasing or always decreasing.<\/p>\n<p>A function is monotonic if it preserves the order of the input values. That is, if \\(x\\) is less than \\(y\\) then the function value at \\(x\\) is always less than the function value at \\(y\\).<\/p>\n<p>A monotonic function is also continuous.<\/p>\n<p>Some examples of monotonic functions are:<\/p>\n<p>\\(f(x) = x^2\\)<\/p>\n<p>\\(f(x) = x\\)<\/p>\n<p>\\(f(x) = 2x\\)<\/p>\n<p>\\(f(x) = x^3\\)<\/p>\n<p>\\(f(x) = -x\\)<\/p>\n<p>\\(f(x) = \\frac{1}{x}\\)<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Increasing_and_Decreasing_Functions_Examples\"><\/span>Increasing and Decreasing Functions Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A function is increasing if, for every value of x in the domain of the function, the function produces a value that is larger than the value produced by the function for any preceding value of x in the domain. A function is decreasing if, for every value of x in the domain of the function, the function produces a value that is smaller than the value produced by the function for any preceding value of x in the domain.<\/p>\n<p>The following are examples of increasing and decreasing functions:<\/p>\n<p>x 2 is an increasing function because the value of the function for each value of x in the domain is larger than the value of the function for any preceding value of x.<\/p>\n<p>is an increasing function because the value of the function for each value of x in the domain is larger than the value of the function for any preceding value of x. x is a decreasing function because the value of the function for each value of x in the domain is smaller than the value of the function for any preceding value of x.<\/p>\n<p>x 3 is an increasing function because the value of the function for each value of x in the domain is larger than the value of the function for any preceding value of x.<\/p>\n<p>is an increasing function because the value of the function for each value of x in the domain is larger than the value of the function for any preceding value of x. x is a decreasing function because the value of the function for each value of x in the domain is smaller than<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Monotonically_Increasing_Functions\"><\/span>Monotonically Increasing Functions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A monotonically increasing function is a function that either always increases or never decreases.<\/p>\n<p>For example, the function y = x2 is monotonically increasing because as x gets larger, y gets larger as well.<\/p>\n<p>The function y = x is not monotonically increasing because as x gets larger, y can get either larger or smaller.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Monotonically_Increasing_Function_Example\"><\/span>Monotonically Increasing Function Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The function y = x is monotonically increasing.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Monotonically_Decreasing_Function\"><\/span>Monotonically Decreasing Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A monotonically decreasing function is a function that always decreases as it moves from left to right.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Monotonically_Decreasing_Function_Example\"><\/span>Monotonically Decreasing Function Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A monotonically decreasing function is one that always decreases as you move from one point to the next. A good example of this is the temperature of water as it moves from a pot on the stove to a glass on the counter. The temperature of the water always decreases as it moves from the pot to the glass.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Tips_to_Study_Increasing_and_Decreasing_Functions_and_Monotonicity\"><\/span>Tips to Study Increasing and Decreasing Functions and Monotonicity<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. Understand what a function is and what it represents.<\/p>\n<p>2. Understand what increasing and decreasing functions are.<\/p>\n<p>3. Understand what monotonicity is and how to determine if a function is monotonic.<\/p>\n<p>4. Practice identifying increasing and decreasing functions and monotonic functions.<\/p>\n<p>5. Understand how to use inverse functions to solve problems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An Introduction to the Internet of Things The internet of things (IoT) is a term for the ever-growing network of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Increasing And Decreasing Functions And Monotonicity","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Increasing And Decreasing Functions And Monotonicity topic of Maths in details explained by subject experts on infinitylearn.com","custom_permalink":"maths\/increasing-and-decreasing-functions-and-monotonicity\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Increasing And Decreasing Functions And Monotonicity - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Increasing And Decreasing Functions And Monotonicity topic of Maths in details explained by subject experts on infinitylearn.com\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/increasing-and-decreasing-functions-and-monotonicity\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Increasing And Decreasing Functions And Monotonicity - 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