{"id":179873,"date":"2025-01-02T18:07:51","date_gmt":"2025-01-02T18:07:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=179873"},"modified":"2025-01-02T18:07:53","modified_gmt":"2025-01-02T18:07:53","slug":"which-of-the-following-rational-functions-is-graphed-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/02\/which-of-the-following-rational-functions-is-graphed-below\/","title":{"rendered":"Which of the following rational functions is graphed below"},"content":{"rendered":"\n

Which of the following rational functions is graphed below?<\/p>\n\n\n\n

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

A. F(x) = 1\/(x + 2)<\/p>\n\n\n\n

B. F(x) = 1\/(x – 2)<\/p>\n\n\n\n

C. F(x) = 1\/2x<\/p>\n\n\n\n

D. F(x) = 2\/X<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To determine which rational function matches the graph, let\u2019s analyze its key features:<\/p>\n\n\n\n

Key Features to Identify:<\/h3>\n\n\n\n
    \n
  1. Vertical Asymptote<\/strong>:\n
      \n
    • Occurs where the denominator equals zero (function is undefined).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Horizontal Asymptote<\/strong>:\n
        \n
      • Found by considering the behavior of the function as xx approaches infinity or negative infinity.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Symmetry<\/strong>:\n
          \n
        • Check if the function is symmetric about the origin (odd function) or symmetric about the y-axis (even function).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Behavior near the Asymptotes<\/strong>:\n
            \n
          • Observe how the function approaches the asymptotes (increases or decreases).<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

            Evaluate Each Option:<\/h3>\n\n\n\n
              \n
            • F(x)=1x+2F(x) = \\frac{1}{x+2}:\n
                \n
              • Vertical asymptote at x=\u22122x = -2, horizontal asymptote at y=0y = 0.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • F(x)=1x\u22122F(x) = \\frac{1}{x-2}:\n
                  \n
                • Vertical asymptote at x=2x = 2, horizontal asymptote at y=0y = 0.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                • F(x)=12xF(x) = \\frac{1}{2x}:\n
                    \n
                  • Vertical asymptote at x=0x = 0, horizontal asymptote at y=0y = 0.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                  • F(x)=2xF(x) = \\frac{2}{x}:\n
                      \n
                    • Vertical asymptote at x=0x = 0, horizontal asymptote at y=0y = 0.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

                      Steps:<\/h3>\n\n\n\n
                        \n
                      1. Identify the location of the vertical asymptote from the graph.<\/li>\n\n\n\n
                      2. Determine how the graph behaves near the asymptotes and at large positive\/negative xx.<\/li>\n<\/ol>\n\n\n\n

                        If you can describe the graph’s asymptotes and behavior (e.g., the vertical asymptote is at x=2x=2, and it approaches zero at large xx), I can match it to one of the functions!<\/p>\n","protected":false},"excerpt":{"rendered":"

                        Which of the following rational functions is graphed below? A. F(x) = 1\/(x + 2) B. F(x) = 1\/(x – 2) C. F(x) = 1\/2x D. F(x) = 2\/X The correct answer and explanation is: To determine which rational function matches the graph, let\u2019s analyze its key features: Key Features to Identify: Evaluate Each Option: […]<\/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-179873","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179873","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=179873"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179873\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=179873"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=179873"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=179873"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}