{"id":179459,"date":"2024-12-31T07:11:51","date_gmt":"2024-12-31T07:11:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=179459"},"modified":"2024-12-31T07:11:54","modified_gmt":"2024-12-31T07:11:54","slug":"consider-the-rational-function","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/12\/31\/consider-the-rational-function\/","title":{"rendered":"Consider the rational function"},"content":{"rendered":"\n<p>Consider the rational function, 2x13x15 What is(ure) the non-permissible value(s) for this rational function? Describe the behaviour of the graph of this function as x approaches each side of each of the non-permissible value(s).<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The rational function you are referring to is ( \\frac{2x}{13x + 15} ). To identify the non-permissible values, we need to determine when the denominator equals zero because division by zero is undefined.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Set the denominator equal to zero:<\/h3>\n\n\n\n<p>[<br>13x + 15 = 0<br>]<br>Now, solve for ( x ):<br>[<br>13x = -15<br>]<br>[<br>x = \\frac{-15}{13}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Non-Permissible Value:<\/h3>\n\n\n\n<p>The non-permissible value for this function is ( x = \\frac{-15}{13} ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Analyze the behavior of the function as ( x ) approaches ( \\frac{-15}{13} ) from each side:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>As ( x \\to \\frac{-15}{13}^- ) (from the left), the denominator ( 13x + 15 ) becomes a small negative number (since ( x ) is slightly less than ( \\frac{-15}{13} ), making ( 13x + 15 ) slightly negative), and the numerator ( 2x ) is negative as well. Thus, the function will approach negative infinity.<\/li>\n\n\n\n<li>As ( x \\to \\frac{-15}{13}^+ ) (from the right), the denominator ( 13x + 15 ) becomes a small positive number (since ( x ) is slightly greater than ( \\frac{-15}{13} ), making ( 13x + 15 ) slightly positive), and the numerator ( 2x ) is still negative. Therefore, the function will approach positive infinity.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Summary of Graph Behavior:<\/h3>\n\n\n\n<p>At ( x = \\frac{-15}{13} ), the function has a vertical asymptote, meaning that the graph approaches infinity on one side and negative infinity on the other side. This is a classic behavior for rational functions when the denominator is zero.<\/p>\n\n\n\n<p>Thus, the graph of the function will show a vertical asymptote at ( x = \\frac{-15}{13} ), and as ( x ) approaches this point from the left, the function heads toward negative infinity, while as ( x ) approaches from the right, it heads toward positive infinity.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider the rational function, 2x13x15 What is(ure) the non-permissible value(s) for this rational function? Describe the behaviour of the graph of this function as x approaches each side of each of the non-permissible value(s). The Correct Answer and Explanation is : The rational function you are referring to is ( \\frac{2x}{13x + 15} ). 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-179459","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179459","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=179459"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179459\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=179459"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=179459"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=179459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}