{"id":249769,"date":"2025-07-09T20:59:32","date_gmt":"2025-07-09T20:59:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249769"},"modified":"2025-07-09T20:59:34","modified_gmt":"2025-07-09T20:59:34","slug":"relation-is-a-function","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/09\/relation-is-a-function\/","title":{"rendered":"Relation is a function"},"content":{"rendered":"\n<p>Relation is a function<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-353.png\" alt=\"\" class=\"wp-image-249770\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is the graph located in the&nbsp;<strong>top right corner<\/strong>.<\/p>\n\n\n\n<p>To determine which of the graphed relations is a function, we must use the definition of a function. A relation is considered a function if and only if every input value (x-value) corresponds to exactly one unique output value (y-value). A simple and reliable way to check this on a graph is by using the Vertical Line Test.<\/p>\n\n\n\n<p>The Vertical Line Test states that if you can draw a vertical line anywhere on the graph that intersects the curve at more than one point, the relation is not a function. This is because a single vertical line represents a constant x-value, and multiple intersection points would mean that one x-value has multiple y-values, violating the core rule of functions.<\/p>\n\n\n\n<p>Let&#8217;s apply this test to each of the four graphs:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Top Left Graph (Circle):<\/strong>\u00a0If you draw a vertical line through any part of the circle&#8217;s interior, for example at x = 1, the line will intersect the circle at two distinct points. Since one x-value corresponds to two y-values, this relation is not a function.<\/li>\n\n\n\n<li><strong>Bottom Left Graph (Sideways Parabola):<\/strong>\u00a0Similar to the circle, a vertical line drawn to the right of the y-axis, such as at x = 2, will cross the parabola in two places. This means it fails the Vertical Line Test and is not a function.<\/li>\n\n\n\n<li><strong>Bottom Right Graph (Vertical Line):<\/strong>\u00a0This graph represents a single x-value that is paired with an infinite number of y-values. A vertical line drawn directly on top of this graph would touch it at every point. This is a clear violation of the function definition.<\/li>\n\n\n\n<li><strong>Top Right Graph (S-shaped Curve):<\/strong>\u00a0If you scan a vertical line across this entire graph from left to right, you will find that the line only ever intersects the curve at a single point. For every x-value, there is only one corresponding y-value. This graph successfully passes the Vertical Line Test.<\/li>\n<\/ol>\n\n\n\n<p>Therefore, the only relation that represents a function is the one depicted in the top right corner.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-52.jpeg\" alt=\"\" class=\"wp-image-249772\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Relation is a function The Correct Answer and Explanation is: The correct answer is the graph located in the&nbsp;top right corner. To determine which of the graphed relations is a function, we must use the definition of a function. A relation is considered a function if and only if every input value (x-value) corresponds to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-249769","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249769","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=249769"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249769\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249769"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249769"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249769"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}