{"id":213976,"date":"2025-05-13T08:37:43","date_gmt":"2025-05-13T08:37:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=213976"},"modified":"2025-05-13T08:37:46","modified_gmt":"2025-05-13T08:37:46","slug":"which-equation-represents-the-function-graphed-on-the-coordinate-plane-gxx4-2-gxx-4-2-gxx-2-4-gxx-24-mark-this-and-return","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/13\/which-equation-represents-the-function-graphed-on-the-coordinate-plane-gxx4-2-gxx-4-2-gxx-2-4-gxx-24-mark-this-and-return\/","title":{"rendered":". Which equation represents the function graphed on the coordinate plane? g(x)=|x+4|-2 g(x)=|x-4|-2 g(x)=|x-2|-4 g(x)=|x-2|+4 Mark this and return"},"content":{"rendered":"\n

. Which equation represents the function graphed on the coordinate plane? g(x)=|x+4|-2 g(x)=|x-4|-2 g(x)=|x-2|-4 g(x)=|x-2|+4 Mark this and return<\/p>\n\n\n\n

    \n
  1. Check all equations that are equivalent.<\/li>\n<\/ol>\n\n\n\n

    a=180(n-2)
    n=(a)\/(180)+1
    n=(a)\/(180)+2
    n=(a+360)\/(180)<\/p>\n\n\n\n

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

    Let’s work through both questions one by one:<\/p>\n\n\n\n

    \n\n\n\n

    Question 1: Which equation represents the function graphed on the coordinate plane?<\/strong><\/h3>\n\n\n\n

    Since you did not provide an image of the graph, I will explain how to identify the correct equation if you’re looking at a graph of an absolute value function<\/strong>.<\/p>\n\n\n\n

    An absolute value function<\/strong> is in the general form: g(x)=\u2223x\u2212h\u2223+kg(x) = |x – h| + k<\/p>\n\n\n\n

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

      \n
    • hh determines the horizontal shift<\/strong> (left or right),<\/li>\n\n\n\n
    • kk determines the vertical shift<\/strong> (up or down),<\/li>\n\n\n\n
    • The vertex<\/strong> of the V-shaped graph is located at the point (h,k)(h, k).<\/li>\n<\/ul>\n\n\n\n

      To determine the correct equation:<\/p>\n\n\n\n

        \n
      • Find the vertex<\/strong> on the graph. This is the point where the “V” changes direction.<\/li>\n\n\n\n
      • Plug that vertex into the standard form g(x)=\u2223x\u2212h\u2223+kg(x) = |x – h| + k, adjusting signs accordingly.<\/li>\n<\/ul>\n\n\n\n

        Let\u2019s look at the answer choices:<\/p>\n\n\n\n

          \n
        1. g(x) = |x + 4| – 2<\/strong> \u2192 Vertex is at (-4, -2)<\/li>\n\n\n\n
        2. g(x) = |x – 4| – 2<\/strong> \u2192 Vertex is at (4, -2)<\/li>\n\n\n\n
        3. g(x) = |x – 2| – 4<\/strong> \u2192 Vertex is at (2, -4)<\/li>\n\n\n\n
        4. g(x) = |x – 2| + 4<\/strong> \u2192 Vertex is at (2, 4)<\/li>\n<\/ol>\n\n\n\n

          So, find the vertex on the graph and match it with the equation’s vertex. For example, if the vertex is at (4, -2), then the correct answer is g(x) = |x – 4| – 2<\/strong>.<\/p>\n\n\n\n

          \n\n\n\n

          Question 2: Check all equations that are equivalent.<\/strong><\/h3>\n\n\n\n

          Given:<\/p>\n\n\n\n

            \n
          1. a=180(n\u22122)a = 180(n – 2) \u2014 This is the formula for the sum of interior angles in a polygon with nn sides.<\/li>\n\n\n\n
          2. n=a180+1n = \\frac{a}{180} + 1<\/li>\n\n\n\n
          3. n=a180+2n = \\frac{a}{180} + 2<\/li>\n\n\n\n
          4. n=a+360180n = \\frac{a + 360}{180}<\/li>\n<\/ol>\n\n\n\n

            We will check which equations are equivalent to the first one.<\/p>\n\n\n\n

            Step-by-step:<\/h4>\n\n\n\n

            Start with: a=180(n\u22122)a = 180(n – 2)<\/p>\n\n\n\n

            Now solve for nn: a180=n\u22122\u21d2n=a180+2\\frac{a}{180} = n – 2 \\Rightarrow n = \\frac{a}{180} + 2<\/p>\n\n\n\n

            So the correct rearranged version of the formula is:<\/p>\n\n\n\n

            n = (a\/180) + 2<\/strong> \u2192 This one IS<\/strong> equivalent.<\/p>\n\n\n\n

            Now test each:<\/p>\n\n\n\n

              \n
            • n=a180+2\\boxed{n = \\frac{a}{180} + 2} \u2192 \u2705 Correct<\/li>\n\n\n\n
            • n=a180+1n = \\frac{a}{180} + 1 \u2192 \u274c Incorrect (off by 1)<\/li>\n\n\n\n
            • n=a+360180n = \\frac{a + 360}{180} \u2192 Check: a+360180=180(n\u22122)+360180=180n\u2212360+360180=180n180=n\\frac{a + 360}{180} = \\frac{180(n – 2) + 360}{180} = \\frac{180n – 360 + 360}{180} = \\frac{180n}{180} = n So this is also correct<\/strong> \u2192 \u2705<\/li>\n<\/ul>\n\n\n\n

              \u2705 Correct equivalent equations:<\/h3>\n\n\n\n
                \n
              • n=a180+2n = \\frac{a}{180} + 2<\/li>\n\n\n\n
              • n=a+360180n = \\frac{a + 360}{180}<\/li>\n<\/ul>\n\n\n\n
                \n\n\n\n

                \u2705 Final Answers:<\/h3>\n\n\n\n

                Question 1<\/strong>: Choose the equation whose vertex matches the graph. Use the vertex to determine the correct option.<\/p>\n\n\n\n

                Question 2<\/strong>: The equivalent equations are:<\/p>\n\n\n\n

                  \n
                • n=a180+2n = \\frac{a}{180} + 2<\/li>\n\n\n\n
                • n=a+360180n = \\frac{a + 360}{180}<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

                  . Which equation represents the function graphed on the coordinate plane? g(x)=|x+4|-2 g(x)=|x-4|-2 g(x)=|x-2|-4 g(x)=|x-2|+4 Mark this and return a=180(n-2)n=(a)\/(180)+1n=(a)\/(180)+2n=(a+360)\/(180) The Correct Answer and Explanation is: Let’s work through both questions one by one: Question 1: Which equation represents the function graphed on the coordinate plane? Since you did not provide an image of the […]<\/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-213976","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213976","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=213976"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213976\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=213976"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=213976"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=213976"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}