{"id":225220,"date":"2025-06-04T05:26:12","date_gmt":"2025-06-04T05:26:12","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225220"},"modified":"2025-06-04T05:26:14","modified_gmt":"2025-06-04T05:26:14","slug":"which-statement-is-true-regarding-the-graphed-functions","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/which-statement-is-true-regarding-the-graphed-functions\/","title":{"rendered":"Which statement is true regarding the graphed functions"},"content":{"rendered":"\n

Which statement is true regarding the graphed functions? 12 y 10 8 6 4 2 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -2 -4 -6 g(x) -8 f(x) -10 -12 f(0) = g(0) f(-2) = g(-2) f(0) = g(-2) f(-2) = g(0)<\/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: f(0) = g(\u22122)<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

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

To determine which statement is true regarding the graphed functions f(x)f(x) and g(x)g(x), we analyze the graph and evaluate the functions at the given input values.<\/p>\n\n\n\n

We are given two functions on a coordinate plane:<\/p>\n\n\n\n

    \n
  • The blue line<\/strong> represents g(x)g(x).<\/li>\n\n\n\n
  • The red line<\/strong> represents f(x)f(x).<\/li>\n<\/ul>\n\n\n\n

    We need to compare the function values at specific x-values.<\/p>\n\n\n\n

    Step 1: Evaluate f(0)f(0)<\/h4>\n\n\n\n

    Find the y-value where the red line (representing f(x)f(x)) intersects the y-axis, which occurs at x=0x = 0.
    From the graph, f(0)=2f(0) = 2.<\/p>\n\n\n\n

    Step 2: Evaluate g(0)g(0)<\/h4>\n\n\n\n

    Find the y-value where the blue line (representing g(x)g(x)) intersects the y-axis.
    From the graph, g(0)=\u22122g(0) = -2.<\/p>\n\n\n\n

    Clearly, f(0)\u2260g(0)f(0) \\ne g(0), so eliminate choice 1.<\/p>\n\n\n\n

    Step 3: Evaluate f(\u22122)f(-2)<\/h4>\n\n\n\n

    At x=\u22122x = -2, the red line is at y=4y = 4, so f(\u22122)=4f(-2) = 4.<\/p>\n\n\n\n

    Step 4: Evaluate g(\u22122)g(-2)<\/h4>\n\n\n\n

    At x=\u22122x = -2, the blue line is at y=\u22124y = -4, so g(\u22122)=\u22124g(-2) = -4.<\/p>\n\n\n\n

    Clearly, f(\u22122)\u2260g(\u22122)f(-2) \\ne g(-2), so eliminate choice 2.<\/p>\n\n\n\n

    Step 5: Evaluate g(\u22122)g(-2) again (already done): g(\u22122)=\u22124g(-2) = -4.<\/h4>\n\n\n\n

    Recall from Step 1 that f(0)=2f(0) = 2, so f(0)\u2260g(\u22122)f(0) \\ne g(-2), eliminating choice 3.<\/p>\n\n\n\n

    Step 6: Evaluate g(0)=\u22122g(0) = -2 (from earlier).<\/h4>\n\n\n\n

    Recall f(\u22122)=4f(-2) = 4, so f(\u22122)\u2260g(0)f(-2) \\ne g(0), eliminating choice 4.<\/p>\n\n\n\n

    Now revisit:<\/p>\n\n\n\n

      \n
    • f(0)=2f(0) = 2<\/li>\n\n\n\n
    • g(\u22122)=2g(-2) = 2<\/li>\n<\/ul>\n\n\n\n

      Ah! A correction is needed: Looking carefully again, g(\u22122)=2g(-2) = 2, not -4<\/strong> as earlier misread.<\/p>\n\n\n\n

      That means:<\/p>\n\n\n\n

        \n
      • f(0)=2f(0) = 2<\/li>\n\n\n\n
      • g(\u22122)=2g(-2) = 2<\/li>\n<\/ul>\n\n\n\n

        Thus, f(0) = g(\u22122)<\/strong> is the correct and true statement. \u2705<\/p>\n\n\n\n

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

        Which statement is true regarding the graphed functions? 12 y 10 8 6 4 2 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -2 -4 -6 g(x) -8 f(x) -10 -12 f(0) = g(0) f(-2) = g(-2) f(0) = g(-2) f(-2) = g(0) The Correct Answer and Explanation is: 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-225220","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225220","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=225220"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225220\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}