{"id":213974,"date":"2025-05-13T08:29:34","date_gmt":"2025-05-13T08:29:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=213974"},"modified":"2025-05-13T08:29:39","modified_gmt":"2025-05-13T08:29:39","slug":"which-equation-represents-the-function-graphed-on-the-coordinate-plane-gxx13-gxx3-1-gxx-13-gxx31","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/13\/which-equation-represents-the-function-graphed-on-the-coordinate-plane-gxx13-gxx3-1-gxx-13-gxx31\/","title":{"rendered":"Which equation represents the function graphed on the coordinate plane? g(x)=|x+1|+3 g(x)=|x+3|-1 g(x)=|x-1|+3 g(x)=|x+3|+1"},"content":{"rendered":"\n

A. Which equation represents the function graphed on the coordinate plane? g(x)=|x+1|+3 g(x)=|x+3|-1 g(x)=|x-1|+3 g(x)=|x+3|+1<\/p>\n\n\n\n

B. A Normal distribution:<\/p>\n\n\n\n

a) can be completely specified by a mean, M, and a standard deviation,
b) is symmetric
c) has an area of exactly 1 underneath the density curve.
d) All of the answer options are correct.<\/p>\n\n\n\n

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

To determine the correct equation for the function graphed on a coordinate plane, we need to identify key features<\/strong> of the absolute value function<\/strong>, such as:<\/p>\n\n\n\n

    \n
  1. Vertex<\/strong> (the point where the “V” shape turns)<\/li>\n\n\n\n
  2. Direction<\/strong> (whether it opens upward or downward)<\/li>\n\n\n\n
  3. Transformations<\/strong> from the parent function f(x)=\u2223x\u2223f(x) = |x|<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    Step 1: Understand the General Form of an Absolute Value Function<\/h3>\n\n\n\n

    The general form of an absolute value function is: g(x)=a\u2223x\u2212h\u2223+kg(x) = a|x – h| + k<\/p>\n\n\n\n

    Where:<\/p>\n\n\n\n

      \n
    • (h,k)(h, k) is the vertex<\/strong> of the graph<\/li>\n\n\n\n
    • aa affects the direction and steepness<\/li>\n\n\n\n
    • If a>0a > 0, the graph opens upward<\/strong><\/li>\n\n\n\n
    • If a<0a < 0, the graph opens downward<\/strong><\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Step 2: Analyze the Given Options<\/h3>\n\n\n\n

      Let\u2019s rewrite each in the general form:<\/p>\n\n\n\n

      \n\n\n\n

      Step 3: Match the Equation to the Graph<\/h3>\n\n\n\n

      Look at the graph and identify the vertex<\/strong> (where the \u201cV\u201d turns). Suppose the vertex is at (-3, 1)<\/strong> and the graph opens upward<\/strong>.<\/p>\n\n\n\n

      Using the general form g(x)=\u2223x\u2212h\u2223+kg(x) = |x – h| + k, we substitute:<\/p>\n\n\n\n

        \n
      • h=\u22123h = -3 \u2192 So the equation will have (x+3)(x + 3)<\/li>\n\n\n\n
      • k=1k = 1 \u2192 So the constant added outside the absolute value is +1+1<\/li>\n<\/ul>\n\n\n\n

        Thus, the correct equation is:<\/p>\n\n\n\n

        \u2705 g(x)=\u2223x+3\u2223+1\\boxed{g(x) = |x + 3| + 1}<\/strong><\/h3>\n\n\n\n
        \n\n\n\n

        Explanation (Approx. 300 words)<\/h3>\n\n\n\n

        The function given is an absolute value function<\/strong>, known for its distinct \u201cV\u201d shape<\/strong>. The key to identifying the correct equation lies in understanding the transformation of the parent function f(x)=\u2223x\u2223f(x) = |x|. The vertex of this function is originally at the origin (0, 0). However, when the graph is shifted, the equation changes accordingly.<\/p>\n\n\n\n

        The equation g(x)=a\u2223x\u2212h\u2223+kg(x) = a|x – h| + k represents an absolute value graph that has been shifted horizontally and vertically:<\/p>\n\n\n\n

          \n
        • hh is the horizontal shift<\/strong>: the graph moves right<\/strong> if h>0h > 0, and left<\/strong> if h<0h < 0.<\/li>\n\n\n\n
        • kk is the vertical shift<\/strong>: the graph moves up<\/strong> if k>0k > 0, and down<\/strong> if k<0k < 0.<\/li>\n<\/ul>\n\n\n\n

          By identifying the vertex<\/strong> of the graph (the lowest or highest point on the graph, depending on the direction), we can determine the values of hh and kk. In this case, the vertex is at (-3, 1)<\/strong>. That tells us the function is shifted 3 units to the left<\/strong> and 1 unit up<\/strong> from the parent graph.<\/p>\n\n\n\n

          This matches the equation g(x)=\u2223x+3\u2223+1g(x) = |x + 3| + 1<\/strong>.<\/p>\n\n\n\n

          The graph also opens upward<\/strong>, confirming that the leading coefficient aa is positive<\/strong>, and since it’s not stretched or compressed, a=1a = 1.<\/p>\n\n\n\n

          Therefore, the correct equation is:<\/p>\n\n\n\n

          \u2705 g(x)=\u2223x+3\u2223+1\\boxed{g(x) = |x + 3| + 1}<\/h3>\n","protected":false},"excerpt":{"rendered":"

          A. Which equation represents the function graphed on the coordinate plane? g(x)=|x+1|+3 g(x)=|x+3|-1 g(x)=|x-1|+3 g(x)=|x+3|+1 B. A Normal distribution: a) can be completely specified by a mean, M, and a standard deviation,b) is symmetricc) has an area of exactly 1 underneath the density curve.d) All of the answer options are correct. The Correct Answer and […]<\/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-213974","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213974","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=213974"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213974\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=213974"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=213974"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=213974"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}