{"id":153878,"date":"2022-03-25T22:54:45","date_gmt":"2022-03-25T17:24:45","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/step-function-definition-explanation-and-properties\/"},"modified":"2024-01-20T16:41:02","modified_gmt":"2024-01-20T11:11:02","slug":"step-function-definition-explanation-and-properties","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/step-function\/","title":{"rendered":"Step Function"},"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\/step-function\/#Introduction_to_Step_Function\" title=\"Introduction to Step Function\">Introduction to Step Function<\/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\/step-function\/#Basic_Definition_of_the_Step_Function\" title=\"Basic Definition of the Step Function\">Basic Definition of the Step Function<\/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\/step-function\/#What_is_Unit_Step\" title=\"What is Unit Step?\">What is Unit Step?<\/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\/step-function\/#Derivative_of_Step_Function\" title=\"Derivative of Step Function\">Derivative of Step Function<\/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\/step-function\/#Integral_of_Step_Function\" title=\"Integral of Step Function\">Integral of Step Function<\/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\/step-function\/#Unit_Step_Function_Graph\" title=\"Unit Step Function Graph\">Unit Step Function Graph<\/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\/step-function\/#Properties_of_Step_Function\" title=\"Properties of Step Function\">Properties of Step Function<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_Step_Function\"><\/span>Introduction to Step Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A Step function is a mathematical function that takes a finite number of discrete steps, rather than a continuous range of values. It is represented by a graph that has a series of horizontal lines, rather than a smooth curve. Step functions are used to model situations where there is a sudden change in the input, such as when a light is turned on or off.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-153877 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/step-function-definition-explanation-and-properties.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/step-function-definition-explanation-and-properties.jpg?v=1648229083 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/step-function-definition-explanation-and-properties-300x212.jpg?v=1648229083 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Basic_Definition_of_the_Step_Function\"><\/span>Basic Definition of the Step Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The step function is a mathematical function that has a discontinuity at a specific point in its domain. This function is also known as the Heaviside function, and it is used to model discontinuous events or processes. The step function is defined as follows:<\/p>\n<p>h(x) = {<br \/>\n0, if x \u2264 0<br \/>\n1, if x &gt; 0<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Unit_Step\"><\/span>What is Unit Step?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Unit step is a mathematical function that produces a discontinuous pulse at its single argument. It is also known as the Heaviside function, after its discoverer, Oliver Heaviside.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Derivative_of_Step_Function\"><\/span>Derivative of Step Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The derivative of the step function is the derivative of the function at 0.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Integral_of_Step_Function\"><\/span>Integral of Step Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The integral of a step function is the area under the curve.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Unit_Step_Function_Graph\"><\/span>Unit Step Function Graph<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A step function is a discontinuous function that has a sharp rise or fall. It is represented by a graph that looks like a staircase.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties_of_Step_Function\"><\/span>Properties of Step Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>A step function is a discontinuous function.<\/li>\n<li>A step function is a function that has a jump discontinuity at one or more points.<\/li>\n<li>A step function is a function that is continuous except at isolated points where it has a jump discontinuity.<\/li>\n<li>A step function can be represented by a graph that has a series of horizontal lines segments.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introduction to Step Function A Step function is a mathematical function that takes a finite number of discrete steps, rather [&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":"Step Function","_yoast_wpseo_title":"Step Function \u2013 Definition, Explanation and Properties","_yoast_wpseo_metadesc":"Learn about step function topic of maths in details explained by subject experts on infinitylearn.com. 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