{"id":191328,"date":"2025-02-14T19:10:55","date_gmt":"2025-02-14T19:10:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=191328"},"modified":"2025-02-14T19:10:59","modified_gmt":"2025-02-14T19:10:59","slug":"unit-3-functions-linear-equations-homework-1","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/14\/unit-3-functions-linear-equations-homework-1\/","title":{"rendered":"Unit 3: Functions & Linear Equations Homework 1"},"content":{"rendered":"\n

Unit 3: Functions & Linear Equations Homework 1: Relations & Functions Name: Bell:_ Date: “* This is a 2-page document! Find the domain and range, then represent as a table, mapping, and graph. 1\/(-5,4), (4,-1), (-2, 1), (O, 4), (1, 3)} Domain Range = Domain s Range = Determine the domain and range of the following continuous graphs. 3. Domain Range 5. Domain- Range 6. Domain- Domain Range = Ranges ?<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s go step by step.<\/p>\n\n\n\n

1. Finding the Domain and Range of the Given Set of Points<\/strong><\/h3>\n\n\n\n

The given set of points is: (\u22125,4),(4,\u22121),(\u22122,1),(0,4),(1,3)(-5,4), (4,-1), (-2,1), (0,4), (1,3)<\/p>\n\n\n\n

    \n
  • Domain<\/strong>: The domain consists of all the x-values in the set. {\u22125,4,\u22122,0,1}\\{-5, 4, -2, 0, 1\\}<\/li>\n\n\n\n
  • Range<\/strong>: The range consists of all the y-values in the set. {4,\u22121,1,4,3}\\{4, -1, 1, 4, 3\\} Since 4 appears twice, we only list it once.<\/li>\n<\/ul>\n\n\n\n

    Thus:<\/p>\n\n\n\n

      \n
    • Domain<\/strong> = {\u22125,\u22122,0,1,4}\\{-5, -2, 0, 1, 4\\}<\/li>\n\n\n\n
    • Range<\/strong> = {\u22121,1,3,4}\\{-1, 1, 3, 4\\}<\/li>\n<\/ul>\n\n\n\n

      2. Representing the Data in Different Forms<\/strong><\/h3>\n\n\n\n

      Table Representation<\/strong><\/h4>\n\n\n\n
      x<\/th>y<\/th><\/tr><\/thead>
      -5<\/td>4<\/td><\/tr>
      4<\/td>-1<\/td><\/tr>
      -2<\/td>1<\/td><\/tr>
      0<\/td>4<\/td><\/tr>
      1<\/td>3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Mapping Representation<\/strong><\/h4>\n\n\n\n

      We can represent the mapping as follows: Domain (x-values)Range (y-values)\u2212544\u22121\u2212210413\\begin{array}{c|c} \\textbf{Domain (x-values)} & \\textbf{Range (y-values)} \\\\ -5 & 4 \\\\ 4 & -1 \\\\ -2 & 1 \\\\ 0 & 4 \\\\ 1 & 3 \\\\ \\end{array}<\/p>\n\n\n\n

      In a visual mapping, each x-value is linked to its corresponding y-value.<\/p>\n\n\n\n

      Graph Representation<\/strong><\/h4>\n\n\n\n

      I’ll generate a scatter plot of these points.<\/p>\n\n\n\n

      Here is the graph representation of the given points. Each point is plotted in the coordinate system, and labeled accordingly.<\/p>\n\n\n\n

      \n\n\n\n

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

      A relation<\/strong> is a set of ordered pairs (x,y)(x, y), where each xx-value is associated with a corresponding yy-value. In the given problem, we have a set of five ordered pairs: (\u22125,4),(4,\u22121),(\u22122,1),(0,4),(1,3)(-5,4), (4,-1), (-2,1), (0,4), (1,3). From this, we can determine two key properties: the domain<\/strong> and range<\/strong>.<\/p>\n\n\n\n

        \n
      • The domain<\/strong> consists of all unique xx-values in the relation. Here, the domain is {\u22125,\u22122,0,1,4}\\{-5, -2, 0, 1, 4\\}.<\/li>\n\n\n\n
      • The range<\/strong> consists of all unique yy-values in the relation. Here, the range is {\u22121,1,3,4}\\{-1, 1, 3, 4\\}, noting that the value 4 appears twice but is listed only once.<\/li>\n<\/ul>\n\n\n\n

        To visually represent this relation, we use different formats:<\/p>\n\n\n\n

          \n
        1. Table Representation<\/strong> organizes the values in a structured way, showing which xx-values correspond to which yy-values.<\/li>\n\n\n\n
        2. Mapping Representation<\/strong> links each element in the domain to an element in the range using arrows.<\/li>\n\n\n\n
        3. Graph Representation<\/strong> plots the points on a Cartesian plane, which helps in visualizing the relationship between the variables.<\/li>\n<\/ol>\n\n\n\n

          Understanding relations is fundamental in mathematics, as they form the basis for functions<\/strong>. A function is a special type of relation where each input (xx-value) has exactly one output (yy-value). In this case, since no xx-value is repeated with different yy-values, the given relation is also a function<\/strong>.<\/p>\n\n\n\n

          The ability to determine the domain and range, as well as represent a relation graphically, is crucial in analyzing mathematical models, data sets, and real-world problems. This knowledge is widely applied in disciplines such as physics, engineering, and economics.<\/p>\n\n\n\n

          Let me know if you need further explanations or modifications!<\/p>\n","protected":false},"excerpt":{"rendered":"

          Unit 3: Functions & Linear Equations Homework 1: Relations & Functions Name: Bell:_ Date: “* This is a 2-page document! Find the domain and range, then represent as a table, mapping, and graph. 1\/(-5,4), (4,-1), (-2, 1), (O, 4), (1, 3)} Domain Range = Domain s Range = Determine the domain and range 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-191328","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191328","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=191328"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191328\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=191328"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=191328"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=191328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}