{"id":251741,"date":"2025-07-11T06:26:58","date_gmt":"2025-07-11T06:26:58","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=251741"},"modified":"2025-07-11T06:27:01","modified_gmt":"2025-07-11T06:27:01","slug":"using-the-desmos-website-calculator-sketch-a-graph-of-a-piecewise-function-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/using-the-desmos-website-calculator-sketch-a-graph-of-a-piecewise-function-2\/","title":{"rendered":"Using the Desmos website calculator, sketch a graph of a piecewise function"},"content":{"rendered":"\n

Using the Desmos website calculator, sketch a graph of a piecewise function. Write the domain in interval notation. y = x^2, -1 \u00e2\u2030\u00a4 x \u00e2\u2030\u00a4 1 and y = 3x – 2, 1 \u00e2\u2030\u00a4 x \u00e2\u2030\u00a4 3 Then choose your own functions and show them on the Desmos website calculator graph.<\/p>\n\n\n\n

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

To graph the given piecewise function on Desmos, follow these steps:<\/p>\n\n\n\n

Step-by-Step Instructions:<\/h3>\n\n\n\n
    \n
  1. Open Desmos<\/strong>: Visit the Desmos website<\/a> and open the calculator.<\/li>\n\n\n\n
  2. Input the Piecewise Function<\/strong>:
    • For the first function y=x2y = x^2y=x2 with domain \u22121\u2264x\u22641-1 \\leq x \\leq 1\u22121\u2264x\u22641: iniCopyEdity = {x^2, -1 \u2264 x \u2264 1}<\/code><\/li>
    • For the second function y=3x\u22122y = 3x – 2y=3x\u22122 with domain 1\u2264x\u226431 \\leq x \\leq 31\u2264x\u22643: iniCopyEdity = {3x - 2, 1 \u2264 x \u2264 3}<\/code><\/li><\/ul>You should now see the piecewise function graphed on the Desmos plot.<\/li>\n<\/ol>\n\n\n\n

      Domain in Interval Notation:<\/h3>\n\n\n\n
        \n
      • The domain of the entire piecewise function is the union of the domains of the two individual pieces.\n
          \n
        • For the first piece, the domain is [\u22121,1][-1, 1][\u22121,1].<\/li>\n\n\n\n
        • For the second piece, the domain is [1,3][1, 3][1,3].<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

          Thus, the domain of the piecewise function in interval notation is:
          [\u22121,3][-1, 3][\u22121,3]<\/p>\n\n\n\n

          Explanation:<\/h3>\n\n\n\n
            \n
          1. Graphing y=x2y = x^2y=x2 on [\u22121,1][-1, 1][\u22121,1]<\/strong>:
            This part of the piecewise function represents a parabola. The graph of y=x2y = x^2y=x2 is a U-shaped curve that is symmetric about the y-axis. On the domain [\u22121,1][-1, 1][\u22121,1], the function will plot only the portion between x=\u22121x = -1x=\u22121 and x=1x = 1x=1.<\/li>\n\n\n\n
          2. Graphing y=3x\u22122y = 3x – 2y=3x\u22122 on [1,3][1, 3][1,3]<\/strong>:
            The second part of the piecewise function is a linear function. The slope of the line is 3, and the y-intercept is -2. This means the line will slope upwards as you move from left to right, starting at x=1x = 1x=1 and ending at x=3x = 3x=3.<\/li>\n\n\n\n
          3. Connecting the Two Pieces<\/strong>:
            At x=1x = 1x=1, the two pieces meet because y=x2y = x^2y=x2 at x=1x = 1x=1 equals 1, and y=3x\u22122y = 3x – 2y=3x\u22122 at x=1x = 1x=1 also equals 1. Therefore, there is no jump or discontinuity between the two pieces at x=1x = 1x=1.<\/li>\n<\/ol>\n\n\n\n

            Choosing My Own Functions:<\/h3>\n\n\n\n

            You could choose other functions to display as well. For example:<\/p>\n\n\n\n

              \n
            1. Let y=x2y = x^2y=x2 on the domain [\u22122,0][-2, 0][\u22122,0].<\/li>\n\n\n\n
            2. Let y=4x+1y = 4x + 1y=4x+1 on the domain [0,2][0, 2][0,2].<\/li>\n<\/ol>\n\n\n\n

              On Desmos, you would input:<\/p>\n\n\n\n

               = {x^2, -2 \u2264 x \u2264 0}
              y = {4x + 1, 0 \u2264 x \u2264 2}
              <\/code><\/pre>\n\n\n\n
              This would plot a parabola and a line, with a continuous connection at x=0x = 0x=0<\/p>\n\n\n\n
              \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
              Using the Desmos website calculator, sketch a graph of a piecewise function. Write the domain in interval notation. y = x^2, -1 \u00e2\u2030\u00a4 x \u00e2\u2030\u00a4 1 and y = 3x – 2, 1 \u00e2\u2030\u00a4 x \u00e2\u2030\u00a4 3 Then choose your own functions and show them on the Desmos website calculator graph. 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-251741","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/251741","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=251741"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/251741\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=251741"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=251741"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=251741"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}