{"id":232643,"date":"2025-06-12T04:52:51","date_gmt":"2025-06-12T04:52:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232643"},"modified":"2025-06-12T04:52:54","modified_gmt":"2025-06-12T04:52:54","slug":"express-each-set-in-interval-notation","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/express-each-set-in-interval-notation\/","title":{"rendered":"Express each set in interval notation"},"content":{"rendered":"\n

Express each set in interval notation: (a) WebAssign Number Line (b) WebAssign Number Line<\/p>\n\n\n\n

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

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

(a)<\/strong>
The correct interval no<\/p>\n\n\n\n

tation is:
[0, 4)<\/p>\n\n\n\n

(b)<\/strong>
The correct interval notation is:
(-4, 0]<\/p>\n\n\n\n

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

Interval notation is a method used to represent a range of numbers on the number line. It uses parentheses and square brackets to indicate whether the endpoints of the range are included in the set.<\/p>\n\n\n\n

    \n
  • A\u00a0square bracket\u00a0[\u00a0or\u00a0]<\/strong>\u00a0indicates that the endpoint is\u00a0included<\/strong>\u00a0in the interval. On a number line, this is represented by a\u00a0solid or closed circle (\u25cf)<\/strong>.<\/li>\n\n\n\n
  • A\u00a0parenthesis\u00a0(\u00a0or\u00a0)<\/strong>\u00a0indicates that the endpoint is\u00a0excluded<\/strong>\u00a0from the interval. On a number line, this is represented by a\u00a0hollow or open circle (\u25cb)<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    The notation is always written with the smaller number on the left and the larger number on the right, separated by a comma.<\/p>\n\n\n\n

    Analysis of Part (a)<\/h4>\n\n\n\n
      \n
    1. Identify the Endpoints:<\/strong>\u00a0The shaded region on the number line extends from 0 to 4.<\/li>\n\n\n\n
    2. Examine the Left Endpoint:<\/strong>\u00a0At the number 0, there is a solid, closed circle (\u25cf). This signifies that 0 is included in the set. Therefore, we use a square bracket\u00a0[\u00a0for the left side of the interval.<\/li>\n\n\n\n
    3. Examine the Right Endpoint:<\/strong>\u00a0At the number 4, there is a hollow, open circle (\u25cb). This signifies that 4 is excluded from the set. The set includes all numbers approaching 4, but not 4 itself. Thus, we use a parenthesis\u00a0)\u00a0for the right side of the interval.<\/li>\n<\/ol>\n\n\n\n

      Combining these, the interval notation for the set is [0, 4)<\/strong>. This represents all real numbers x<\/em> such that 0 \u2264 x<\/em> < 4.<\/p>\n\n\n\n

      Analysis of Part (b)<\/h4>\n\n\n\n
        \n
      1. Identify the Endpoints:<\/strong>\u00a0The shaded region on this number line spans from -4 to 0.<\/li>\n\n\n\n
      2. Examine the Left Endpoint:<\/strong>\u00a0At the number -4, there is a hollow, open circle (\u25cb). This indicates that -4 is not part of the set. Accordingly, we start the interval notation with a parenthesis\u00a0(.<\/li>\n\n\n\n
      3. Examine the Right Endpoint:<\/strong>\u00a0At the number 0, there is a solid, closed circle (\u25cf). This means that 0 is included in the set. We close the interval notation with a square bracket\u00a0].<\/li>\n<\/ol>\n\n\n\n

        Combining these, the interval notation for this set is (-4, 0]<\/strong>. This represents all real numbers x<\/em> such that -4 < x<\/em> \u2264 0.thumb_upthumb_down<\/p>\n\n\n\n

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

        Express each set in interval notation: (a) WebAssign Number Line (b) WebAssign Number Line The Correct Answer and Explanation is: (a)The correct interval no tation is:[0, 4) (b)The correct interval notation is:(-4, 0] Explanation Interval notation is a method used to represent a range of numbers on the number line. It uses parentheses and square […]<\/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-232643","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232643","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=232643"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232643\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}