{"id":233654,"date":"2025-06-13T09:43:24","date_gmt":"2025-06-13T09:43:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233654"},"modified":"2025-06-13T09:43:26","modified_gmt":"2025-06-13T09:43:26","slug":"course-apexlearning-com-public-activity-1008003-assessment-019-sem-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/course-apexlearning-com-public-activity-1008003-assessment-019-sem-2\/","title":{"rendered":"course.apexlearning.com\/public\/activity\/1008003\/assessment 019) Sem 2"},"content":{"rendered":"\n<p>course.apexlearning.com\/public\/activity\/1008003\/assessment 019) Sem 2 ?1.8.3 Quiz: Finding Vertical Asymptotes which of the following rational functions is graphed below? -10 10 10 -10 A.<\/p>\n\n\n\n<p>B.<\/p>\n\n\n\n<p>C.<\/p>\n\n\n\n<p>D.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-433.png\" alt=\"\" class=\"wp-image-233655\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer: C. F(x) = 1\/x\u00b2<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>To determine which rational function is represented by the graph, we can analyze the key features of the graph, specifically its vertical asymptotes and its behavior around them.<\/p>\n\n\n\n<p><strong>1. Identifying the Vertical Asymptote:<\/strong><br>A vertical asymptote is a vertical line that the graph of a function approaches but never touches or crosses. It occurs at x-values where the denominator of the rational function is equal to zero, provided the numerator is not also zero at that x-value.<\/p>\n\n\n\n<p>By observing the provided graph, we can see that the function&#8217;s y-values shoot up to positive infinity as the x-values get closer and closer to 0 from both the left and the right sides. This indicates that there is a vertical asymptote at the line&nbsp;<strong>x = 0<\/strong>.<\/p>\n\n\n\n<p><strong>2. Evaluating the Options:<\/strong><br>Now, let&#8217;s examine the denominator of each given function to find its vertical asymptote(s):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A. F(x) = 1 \/ (x + 1)\u00b2:<\/strong>\u00a0The denominator is zero when (x + 1)\u00b2 = 0, which means x = -1. This function has a vertical asymptote at x = -1, which does not match the graph.<\/li>\n\n\n\n<li><strong>B. F(x) = 1 \/ (x &#8211; 1)\u00b2:<\/strong>\u00a0The denominator is zero when (x &#8211; 1)\u00b2 = 0, which means x = 1. This function has a vertical asymptote at x = 1, which does not match the graph.<\/li>\n\n\n\n<li><strong>C. F(x) = 1 \/ x\u00b2:<\/strong>\u00a0The denominator is zero when x\u00b2 = 0, which means x = 0. This function has a vertical asymptote at x = 0, which matches the graph.<\/li>\n\n\n\n<li><strong>D. F(x) = -1 \/ x\u00b2:<\/strong>\u00a0The denominator is zero when x\u00b2 = 0, which means x = 0. This function also has a vertical asymptote at x = 0, matching the graph.<\/li>\n<\/ul>\n\n\n\n<p>Based on the vertical asymptote, we can eliminate options A and B, leaving C and D as possibilities.<\/p>\n\n\n\n<p><strong>3. Analyzing the Function&#8217;s Behavior:<\/strong><br>To choose between C and D, we look at the behavior of the graph. The entire graph lies above the x-axis, which means that the function&#8217;s values, F(x), are always positive for all x in its domain.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>For C. F(x) = 1 \/ x\u00b2:<\/strong>\u00a0The numerator is 1 (a positive number). The denominator, x\u00b2, is always positive for any non-zero real number x. Since a positive number divided by a positive number is always positive, F(x) will always be greater than 0. This matches the graph, where both branches go towards positive infinity.<\/li>\n\n\n\n<li><strong>For D. F(x) = -1 \/ x\u00b2:<\/strong>\u00a0The numerator is -1 (a negative number). The denominator, x\u00b2, is always positive. A negative number divided by a positive number is always negative. This means the graph of this function would lie entirely below the x-axis. This contradicts the given graph.<\/li>\n<\/ul>\n\n\n\n<p><strong>Conclusion:<\/strong><br>The function F(x) = 1\/x\u00b2 is the only option that has a vertical asymptote at x = 0 and produces only positive y-values, perfectly matching the provided graph.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-295.jpeg\" alt=\"\" class=\"wp-image-233656\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>course.apexlearning.com\/public\/activity\/1008003\/assessment 019) Sem 2 ?1.8.3 Quiz: Finding Vertical Asymptotes which of the following rational functions is graphed below? -10 10 10 -10 A. B. C. D. The Correct Answer and Explanation is: Correct Answer: C. F(x) = 1\/x\u00b2 Explanation: To determine which rational function is represented by the graph, we can analyze the key features [&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-233654","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233654","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=233654"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233654\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233654"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233654"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233654"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}