{"id":229794,"date":"2025-06-08T12:34:29","date_gmt":"2025-06-08T12:34:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=229794"},"modified":"2025-06-08T12:34:32","modified_gmt":"2025-06-08T12:34:32","slug":"question-8-of-10-2-points-which-of-the-following-rational-functions-is-graphed-below-1-a","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/question-8-of-10-2-points-which-of-the-following-rational-functions-is-graphed-below-1-a\/","title":{"rendered":"Question 8 of 10 2 Points Which of the following rational functions is graphed below? 1 A."},"content":{"rendered":"\n

<\/p>\n\n\n\n

Question 8 of 10 2 Points Which of the following rational functions is graphed below? 1 A.<\/p>\n\n\n\n

4 B.<\/p>\n\n\n\n

1 C.<\/p>\n\n\n\n

1 D.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is:<\/p>\n\n\n\n

D. F(x)=1(x\u22124)2F(x) = \\frac{1}{(x – 4)^2}F(x)=(x\u22124)21\u200b<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation <\/strong><\/h3>\n\n\n\n

To determine the correct rational function that corresponds to the given graph, we need to analyze the key features of the graph shown:<\/p>\n\n\n\n

1. Vertical Asymptote:<\/strong><\/h4>\n\n\n\n

The graph has a vertical asymptote at x=4x = 4x=4<\/strong>. This occurs in rational functions when the denominator becomes zero (division by zero). So, we are looking for a function whose denominator is zero when x=4x = 4x=4. This rules out:<\/p>\n\n\n\n

    \n
  • Option A: 1(x+4)2\\frac{1}{(x + 4)^2}(x+4)21\u200b \u2192 vertical asymptote at x=\u22124x = -4x=\u22124<\/li>\n\n\n\n
  • Option B: 4×2\\frac{4}{x^2}x24\u200b \u2192 vertical asymptote at x=0x = 0x=0<\/li>\n\n\n\n
  • Option C: 14×2\\frac{1}{4x^2}4×21\u200b \u2192 vertical asymptote at x=0x = 0x=0<\/li>\n<\/ul>\n\n\n\n

    Only Option D<\/strong>, 1(x\u22124)2\\frac{1}{(x – 4)^2}(x\u22124)21\u200b, has a vertical asymptote at x=4x = 4x=4.<\/p>\n\n\n\n

    2. Shape and Behavior:<\/strong><\/h4>\n\n\n\n

    The graph is symmetric around the vertical asymptote, and the function values are always positive<\/strong> (approaching infinity as x\u21924x \\to 4x\u21924 from both sides and decreasing to zero as xxx moves away from 4). This is characteristic of a squared denominator<\/strong> like (x\u22124)2(x – 4)^2(x\u22124)2, which ensures the output is always positive, just like 1×2\\frac{1}{x^2}x21\u200b.<\/p>\n\n\n\n

    3. No x-intercepts:<\/strong><\/h4>\n\n\n\n

    There is no x-intercept (the graph never touches the x-axis), which confirms that the numerator is a non-zero constant (here, 1), and the denominator never causes the output to be zero.<\/p>\n\n\n\n

    Therefore, based on the location of the vertical asymptote and the overall shape of the graph, the rational function that matches the graph is:F(x)=1(x\u22124)2\\boxed{F(x) = \\frac{1}{(x – 4)^2}}F(x)=(x\u22124)21\u200b\u200b<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n
    \"\"<\/figure>\n\n\n\n\n\n
    \"\"<\/figure>\n\n\n\n
    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Question 8 of 10 2 Points Which of the following rational functions is graphed below? 1 A. 4 B. 1 C. 1 D. The Correct Answer and Explanation is: The correct answer is: D. F(x)=1(x\u22124)2F(x) = \\frac{1}{(x – 4)^2}F(x)=(x\u22124)21\u200b Explanation To determine the correct rational function that corresponds to the given graph, we need to […]<\/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-229794","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229794","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=229794"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229794\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=229794"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=229794"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=229794"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}