{"id":160114,"date":"2024-11-02T08:04:40","date_gmt":"2024-11-02T08:04:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=160114"},"modified":"2024-11-02T08:04:43","modified_gmt":"2024-11-02T08:04:43","slug":"which-function-is-shown-in-the-graph-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/02\/which-function-is-shown-in-the-graph-below\/","title":{"rendered":"Which function is shown in the graph below"},"content":{"rendered":"\n

Which function is shown in the graph below?
A) y=(1\/2)^x+3 -1
B) y=(1\/2)^x-3 +1
C) y=(1\/2)^x-1 +3
D) y=(1\/2)^x+1 -3<\/p>\n\n\n\n

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

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

To determine which function is represented by the graph, we need to analyze the key features of the provided options and the graph itself.<\/p>\n\n\n\n

Function Analysis<\/h3>\n\n\n\n
    \n
  1. Form of the Function<\/strong>: All options are in the form (y = a^x + k), where (a) is a base and (k) is a vertical shift. The base is (1\/2), indicating a decreasing exponential function.<\/li>\n\n\n\n
  2. Vertical Shift<\/strong>: The vertical shift (k) affects the horizontal asymptote of the graph. If (k > 0), the asymptote will be (y = k) (above the x-axis), and if (k < 0), it will be (y = k) (below the x-axis).<\/li>\n<\/ol>\n\n\n\n

    Evaluating Options<\/h3>\n\n\n\n
      \n
    • A) (y = (1\/2)^x + 3 – 1 = (1\/2)^x + 2)<\/strong>: The horizontal asymptote is at (y = 2).<\/li>\n\n\n\n
    • B) (y = (1\/2)^x – 3 + 1 = (1\/2)^x – 2)<\/strong>: The horizontal asymptote is at (y = -2).<\/li>\n\n\n\n
    • C) (y = (1\/2)^x – 1 + 3 = (1\/2)^x + 2)<\/strong>: The horizontal asymptote is at (y = 2).<\/li>\n\n\n\n
    • D) (y = (1\/2)^x + 1 – 3 = (1\/2)^x – 2)<\/strong>: The horizontal asymptote is at (y = -2).<\/li>\n<\/ul>\n\n\n\n

      Asymptote Determination<\/h3>\n\n\n\n

      To match with the graph, identify the horizontal asymptote:<\/p>\n\n\n\n

        \n
      • If the graph approaches a specific line as (x) approaches infinity, it indicates the value of (k).<\/li>\n<\/ul>\n\n\n\n

        Conclusion<\/h3>\n\n\n\n

        Assuming the graph’s asymptote is at (y = -2), the correct function would be either B) (y = (1\/2)^x – 2)<\/strong> or D) (y = (1\/2)^x – 2)<\/strong>. Both options provide the same asymptote.<\/p>\n\n\n\n

        In examining the behavior as (x) approaches positive infinity, the graph would decrease towards this line, confirming the match. If the graph displays a shift upwards, options A and C can be eliminated. Thus, you can select option B or D<\/strong>, depending on the specific curve behavior near the asymptote.<\/p>\n\n\n\n

        To finalize which one is correct, observe the specific details in the graph about the intercepts and behavior at x-values approaching zero and positive infinity.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Which function is shown in the graph below?A) y=(1\/2)^x+3 -1B) y=(1\/2)^x-3 +1C) y=(1\/2)^x-1 +3D) y=(1\/2)^x+1 -3 The Correct Answer and Explanation is : To determine which function is represented by the graph, we need to analyze the key features of the provided options and the graph itself. Function Analysis Evaluating Options Asymptote Determination To match […]<\/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-160114","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160114","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=160114"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160114\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=160114"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=160114"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=160114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}