{"id":159698,"date":"2024-11-01T06:56:33","date_gmt":"2024-11-01T06:56:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=159698"},"modified":"2024-11-01T06:56:35","modified_gmt":"2024-11-01T06:56:35","slug":"which-function-has-no-horizontal-asymptote","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/01\/which-function-has-no-horizontal-asymptote\/","title":{"rendered":"Which function has no horizontal asymptote"},"content":{"rendered":"\n<p>Which function has no horizontal asymptote?<\/p>\n\n\n\n<p>A f(x) = 2x-1 3&#215;2 x-1 <\/p>\n\n\n\n<p>B f(x) = 3x 2&#215;2 <\/p>\n\n\n\n<p>C f(x)=3x-1<\/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>To determine which function has no horizontal asymptote, we need to analyze each function&#8217;s behavior as ( x ) approaches infinity (or negative infinity). Horizontal asymptotes indicate the value that a function approaches as the input becomes very large or very small. Let&#8217;s examine each function provided:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Function A: ( f(x) = \\frac{2x &#8211; 1}{3x^2 + x &#8211; 1} )<\/h3>\n\n\n\n<p>To find the horizontal asymptote, we consider the leading terms of the numerator and the denominator:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The leading term of the numerator is ( 2x ).<\/li>\n\n\n\n<li>The leading term of the denominator is ( 3x^2 ).<\/li>\n<\/ul>\n\n\n\n<p>As ( x ) approaches infinity, the function behaves like:<\/p>\n\n\n\n<p>[<br>f(x) \\approx \\frac{2x}{3x^2} = \\frac{2}{3x} \\to 0 \\quad \\text{(as } x \\to \\infty\\text{)}<br>]<\/p>\n\n\n\n<p>Thus, this function has a horizontal asymptote at ( y = 0 ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Function B: ( f(x) = \\frac{3x}{2x^2} )<\/h3>\n\n\n\n<p>Similarly, we analyze this function:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The leading term of the numerator is ( 3x ).<\/li>\n\n\n\n<li>The leading term of the denominator is ( 2x^2 ).<\/li>\n<\/ul>\n\n\n\n<p>As ( x ) approaches infinity, the function behaves like:<\/p>\n\n\n\n<p>[<br>f(x) \\approx \\frac{3x}{2x^2} = \\frac{3}{2x} \\to 0 \\quad \\text{(as } x \\to \\infty\\text{)}<br>]<\/p>\n\n\n\n<p>This function also has a horizontal asymptote at ( y = 0 ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Function C: ( f(x) = 3x &#8211; 1 )<\/h3>\n\n\n\n<p>This function is a linear function. As ( x ) approaches infinity, the function behaves like:<\/p>\n\n\n\n<p>[<br>f(x) \\to 3x &#8211; 1 \\to \\infty \\quad \\text{(as } x \\to \\infty\\text{)}<br>]<\/p>\n\n\n\n<p>Since the output grows indefinitely without approaching a specific finite value, this function does <strong>not<\/strong> have a horizontal asymptote.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The function that has <strong>no horizontal asymptote<\/strong> is <strong>C: ( f(x) = 3x &#8211; 1 )<\/strong>. Linear functions such as this one typically do not have horizontal asymptotes because their value increases or decreases indefinitely as ( x ) approaches infinity or negative infinity, in contrast to rational functions which often settle at specific values determined by their leading coefficients.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which function has no horizontal asymptote? A f(x) = 2x-1 3&#215;2 x-1 B f(x) = 3x 2&#215;2 C f(x)=3x-1 The Correct Answer and Explanation is : To determine which function has no horizontal asymptote, we need to analyze each function&#8217;s behavior as ( x ) approaches infinity (or negative infinity). Horizontal asymptotes indicate the value [&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-159698","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159698","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=159698"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159698\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=159698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=159698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=159698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}