{"id":156286,"date":"2022-03-26T01:35:19","date_gmt":"2022-03-25T20:05:19","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/relations-and-functions-2\/"},"modified":"2023-06-16T18:54:55","modified_gmt":"2023-06-16T13:24:55","slug":"relations-and-functions-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/relations-and-functions\/","title":{"rendered":"Relations and Functions"},"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\/relations-and-functions\/#Explain_the_difference_between_a_relation_and_a_function\" title=\"Explain the difference between a relation and a function.\">Explain the difference between a relation and a 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\/relations-and-functions\/#What_is_a_Function\" title=\"What is a Function?\">What is a Function?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/relations-and-functions\/#Types_of_Functions\" title=\"Types of Functions\">Types of Functions<\/a><\/li><\/ul><\/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\/relations-and-functions\/#Explain_in_Detail_Cartesian_Products_of_Sets\" title=\"Explain in Detail: Cartesian Products of Sets\">Explain in Detail: Cartesian Products of Sets<\/a><\/li><\/ul><\/nav><\/div>\n<p><span style=\"font-size: 14pt;\"><strong>Relations and Functions class 11<\/strong><\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156285 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/relations-and-functions.jpg\" alt=\"Relations and Functions class 11\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/relations-and-functions.jpg?v=1648238714 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/relations-and-functions-300x212.jpg?v=1648238714 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Explain_the_difference_between_a_relation_and_a_function\"><\/span>Explain <span style=\"font-size: 18pt;\"><strong>the difference between a relation and a function.<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A relation is a set of ordered pairs. A function is a relation in which each element in the domain is paired with one and only one element in the range.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Function\"><\/span>What is a Function?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A function is a relation that describes there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.<\/p>\n<p><b>For example:<\/b><\/p>\n<div class=\"table-responsive\">\n<table class=\"table-bordered\">\n<tbody>\n<tr>\n<td>Domain<\/td>\n<td>Range<\/td>\n<\/tr>\n<tr>\n<td>-1<\/td>\n<td>-3<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"table-responsive\">\n<table class=\"table-bordered\">\n<tbody>\n<tr>\n<td><b>Domain<\/b><\/td>\n<td>It is a collection of the first values in the ordered pair (Set of all input (x) values).<\/td>\n<\/tr>\n<tr>\n<td><b>Range<\/b><\/td>\n<td>It is a collection of the second values in the ordered pair (Set of all output (y) values).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><b>Example:<\/b><\/p>\n<p>In the relation, {(-2, 3), {4, 5), (6, -5), (-2, 3)},<\/p>\n<p>The domain is {-2, 4, 6} and range is {-5, 3, 5}.<\/p>\n<p><b>Note<\/b>: Don\u2019t consider duplicates while writing the domain and range and also write it in increasing order.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Types_of_Functions\"><\/span>Types of Functions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>In terms of relations, we can define the types of functions as:<\/p>\n<ul>\n<li><strong>One-to-one function or Injective function:<\/strong> A function f: P \u2192 Q is said to be one-to-one if for each element of P there is a distinct element of Q.<\/li>\n<li><strong>Many-to-one function:<\/strong> A function that maps two or more elements of P to the same element of set Q.<\/li>\n<li><strong>Onto Function or Surjective function: <\/strong>A function for which every element of set Q there is a pre-image in set P<\/li>\n<li><strong>One-one correspondence or Bijective function: <\/strong>The function f matches with each element of P with a discrete element of Q and every element of Q has a pre-image in P.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Explain_in_Detail_Cartesian_Products_of_Sets\"><\/span>Explain in Detail: Cartesian Products of Sets<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A Cartesian product of two sets is a set that is created by pairing every element of the first set with every element of the second set. For example, if the first set consists of the numbers 1, 2, and 3, and the second set consists of the numbers 4, 5, and 6, the Cartesian product of the two sets would be the set {1, 4, 2, 5, 3, 6}.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Relations and Functions class 11 Explain the difference between a relation and a function. A relation is a set 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":"Relations and Functions class 11","_yoast_wpseo_title":"Relation and Function Class 11 | Examples & Differences, Types of Functions","_yoast_wpseo_metadesc":"A function is a relation that describes there should be only one output for each input (or) we can say that a special kind of relation.","custom_permalink":"maths\/relations-and-functions\/"},"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>Relation and Function Class 11 | Examples &amp; Differences, Types of Functions<\/title>\n<meta name=\"description\" content=\"A function is a relation that describes there should be only one output for each input (or) we can say that a 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