{"id":229208,"date":"2025-06-08T04:06:55","date_gmt":"2025-06-08T04:06:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=229208"},"modified":"2025-06-08T04:06:58","modified_gmt":"2025-06-08T04:06:58","slug":"the-graph-of-a-function-h-is-given-y-6-5-4-3-2-654321-23456-a-find-h-2-h0-h2-and-h3-h-2-2-h0-0-h2-4-h3-5-b-find-the-domain-and-range-of-h","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/the-graph-of-a-function-h-is-given-y-6-5-4-3-2-654321-23456-a-find-h-2-h0-h2-and-h3-h-2-2-h0-0-h2-4-h3-5-b-find-the-domain-and-range-of-h\/","title":{"rendered":"The graph of a function h is given. y -6-5-4-3-2 654321 23456 (a) Find h(-2), h(0), h(2), and h(3). h(-2) = 2 h(0) = 0 h(2) = 4 h(3) = 5 (b) Find the domain and range of h"},"content":{"rendered":"\n

The graph of a function h is given. y -6-5-4-3-2 654321 23456 (a) Find h(-2), h(0), h(2), and h(3). h(-2) = 2 h(0) = 0 h(2) = 4 h(3) = 5 (b) Find the domain and range of h. (Enter your answers using interval notation.) domain range (c) Find the values of x for which h(x) = 4. (Enter your answers as a comma-separated list.) x = -3,4 (d) Find the values of x for which h(x) ? 4. (-3, 2) -3, 2, 4 [-3, 2] and 4 [2, 4] and -3 (2, 4) (e) Find the net change in h between x = -3 and x = 3.<\/p>\n\n\n\n

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

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

(a) Evaluating Specific Points<\/h3>\n\n\n\n

You are asked to find values of the function h(x)h(x)h(x) at specific xxx-values using the graph.<\/p>\n\n\n\n

From the graph:<\/p>\n\n\n\n

    \n
  • h(\u22122)=2h(-2) = 2h(\u22122)=2<\/li>\n\n\n\n
  • h(0)=0h(0) = 0h(0)=0<\/li>\n\n\n\n
  • h(2)=4h(2) = 4h(2)=4<\/li>\n\n\n\n
  • h(3)=5h(3) = 5h(3)=5<\/li>\n<\/ul>\n\n\n\n

    \u2705 All values are correctly filled in.<\/p>\n\n\n\n

    \n\n\n\n

    (b) Domain and Range<\/strong><\/h3>\n\n\n\n

    Domain<\/strong>: The domain is the set of all xxx-values for which the function is defined. From the graph, the function starts at x=\u22124x = -4x=\u22124 and ends at x=5x = 5x=5. So:<\/p>\n\n\n\n

      \n
    • Domain<\/strong> = [\u22124,5][ -4, 5 ][\u22124,5]<\/li>\n<\/ul>\n\n\n\n

      Range<\/strong>: The range is the set of all yyy-values the function takes. From the graph, the lowest value of h(x)h(x)h(x) is 0 (at x=0x = 0x=0), and the highest is 6 (at x=4x = 4x=4):<\/p>\n\n\n\n

        \n
      • Range<\/strong> = [0,6][ 0, 6 ][0,6]<\/li>\n<\/ul>\n\n\n\n

        \u274c The previous answer was incorrect. Correct domain: [\u22124,5][ -4, 5 ][\u22124,5], range: [0,6][ 0, 6 ][0,6]<\/p>\n\n\n\n

        \n\n\n\n

        (c) Find xxx such that h(x)=4h(x) = 4h(x)=4<\/strong><\/h3>\n\n\n\n

        Looking at the graph, h(x)=4h(x) = 4h(x)=4 at two points:<\/p>\n\n\n\n

          \n
        • x=2x = 2x=2<\/li>\n\n\n\n
        • x=5x = 5x=5<\/li>\n<\/ul>\n\n\n\n

          \u274c The answer “-3, 4” is incorrect.<\/p>\n\n\n\n

          \u2705 Correct answer: x=2,5x = 2, 5x=2,5<\/strong><\/p>\n\n\n\n

          \n\n\n\n

          (d) Find values of xxx such that h(x)\u22644h(x) \\leq 4h(x)\u22644<\/strong><\/h3>\n\n\n\n

          From the graph, h(x)\u22644h(x) \\leq 4h(x)\u22644 from:<\/p>\n\n\n\n

            \n
          • x=\u22123x = -3x=\u22123 to x=2x = 2x=2 (inclusive),<\/li>\n\n\n\n
          • and again at x=4x = 4x=4 where h(4)=4h(4) = 4h(4)=4.<\/li>\n<\/ul>\n\n\n\n

            \u2705 The correct interval is:
            \u22123,2-3, 2\u22123,2 and x=4x = 4x=4<\/strong><\/p>\n\n\n\n

            So the correct multiple-choice answer is:
            \u22123,2-3, 2\u22123,2 and 4<\/strong><\/p>\n\n\n\n

            \n\n\n\n

            (e) Net Change from x=\u22123x = -3x=\u22123 to x=3x = 3x=3<\/strong><\/h3>\n\n\n\n
              \n
            • h(\u22123)=4h(-3) = 4h(\u22123)=4<\/li>\n\n\n\n
            • h(3)=5h(3) = 5h(3)=5<\/li>\n<\/ul>\n\n\n\n

              Net change<\/strong> = h(3)\u2212h(\u22123)=5\u22124=1h(3) – h(-3) = 5 – 4 = 1h(3)\u2212h(\u22123)=5\u22124=1<\/p>\n\n\n\n

              \u2705 Correct answer: 1<\/strong><\/p>\n\n\n\n

              \n\n\n\n

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

              This problem tests key concepts in reading and interpreting graphs of functions. First, evaluating a function at given points simply involves identifying the y-values at specified x-values on the graph. In (a), locating each x-value on the graph and identifying its corresponding height yields the values for h(x)h(x)h(x).<\/p>\n\n\n\n

              In (b), understanding the domain<\/strong> and range<\/strong> involves recognizing the horizontal and vertical extent of the graph. The domain corresponds to the leftmost to rightmost x-values for which the graph exists, while the range reflects the lowest to highest y-values. Mistakes here often stem from overlooking endpoints or misinterpreting open versus closed intervals.<\/p>\n\n\n\n

              Part (c) requires identifying where the graph intersects a horizontal line y=4y = 4y=4. This involves visually locating points on the graph where the height is 4 and reading the corresponding x-values. This question challenges your ability to link function values to x-coordinates and avoid guessing based on symmetry or estimation.<\/p>\n\n\n\n

              Part (d) examines your understanding of inequalities with functions. You’re not just identifying points where h(x)=4h(x) = 4h(x)=4, but also where the function lies below that level. This tests the ability to read intervals where the graph is beneath or touches a horizontal line.<\/p>\n\n\n\n

              Finally, (e) asks for the net change<\/strong>, calculated as the difference in output values over an interval. This is a fundamental concept in understanding rates of change and comparing function behavior across intervals. Altogether, this exercise blends graphical interpretation with functional reasoning.<\/p>\n\n\n\n

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

              The graph of a function h is given. y -6-5-4-3-2 654321 23456 (a) Find h(-2), h(0), h(2), and h(3). h(-2) = 2 h(0) = 0 h(2) = 4 h(3) = 5 (b) Find the domain and range of h. (Enter your answers using interval notation.) domain range (c) Find the values of x for which […]<\/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-229208","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229208","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=229208"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229208\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=229208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=229208"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=229208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}