{"id":225186,"date":"2025-06-03T21:55:07","date_gmt":"2025-06-03T21:55:07","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225186"},"modified":"2025-06-03T21:55:10","modified_gmt":"2025-06-03T21:55:10","slug":"radical-functions-date","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/radical-functions-date\/","title":{"rendered":"Radical Functions Date"},"content":{"rendered":"\n

Radical Functions Date: Bell: Homework 7: Graphing Radical Functions This is a 2-page document. ** For questions 1-2: Describe the transformations from the parent function f(x) = \u00e2\u02c6\u0161x. 3. The square root parent function is vertically compressed by a factor of 1\/3, then translated so that it has an endpoint located at (4, -1). Write an equation that could represent this function. The cube root parent function is reflected across the x-axis, vertically stretched by a factor of 3, then translated 2 units down. Write an equation that could represent this function.<\/p>\n\n\n\n

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

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

Let’s go through each question and provide correct answers with a clear explanation of the transformations:<\/p>\n\n\n\n

\n\n\n\n

1. f(x)=2x\u22129f(x) = 2\\sqrt{x} – 9<\/strong><\/h3>\n\n\n\n

Transformations from the parent function f(x)=xf(x) = \\sqrt{x}:<\/strong><\/p>\n\n\n\n

    \n
  • Vertical stretch<\/strong> by a factor of 2<\/strong> (multiplies the output by 2).<\/li>\n\n\n\n
  • Vertical translation<\/strong> down 9 units<\/strong> (subtracting 9 from the output).<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    2. f(x)=\u2212x+53+3f(x) = -\\sqrt[3]{x + 5} + 3<\/strong><\/h3>\n\n\n\n

    Transformations from the parent function f(x)=x3f(x) = \\sqrt[3]{x}:<\/strong><\/p>\n\n\n\n

      \n
    • Horizontal shift<\/strong> left 5 units<\/strong> (inside the radical: x+5x + 5).<\/li>\n\n\n\n
    • Reflection<\/strong> over the x-axis<\/strong> (the negative sign in front).<\/li>\n\n\n\n
    • Vertical shift<\/strong> up 3 units<\/strong> (adding 3 to the entire function).<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      3. The square root function is compressed vertically by 13\\frac{1}{3}, and endpoint at (4, -1):<\/strong><\/h3>\n\n\n\n

      The general square root function is:
      f(x)=ax\u2212h+kf(x) = a\\sqrt{x – h} + k
      Where:<\/p>\n\n\n\n

        \n
      • a=13a = \\frac{1}{3} (vertical compression),<\/li>\n\n\n\n
      • (h,k)=(4,\u22121)(h, k) = (4, -1) (endpoint of transformation).<\/li>\n<\/ul>\n\n\n\n

        So the equation is:
        f(x)=13x\u22124\u22121f(x) = \\frac{1}{3} \\sqrt{x – 4} – 1<\/strong><\/p>\n\n\n\n

        \n\n\n\n

        4. The cube root function is reflected over the x-axis, vertically stretched by 3, and translated 2 units down:<\/strong><\/h3>\n\n\n\n

        The general cube root function is:
        f(x)=ax\u2212h3+kf(x) = a\\sqrt[3]{x – h} + k
        Given:<\/p>\n\n\n\n

          \n
        • Reflected over x-axis<\/strong> \u2192 negative sign,<\/li>\n\n\n\n
        • Stretched by 3<\/strong> \u2192 multiply by 3,<\/li>\n\n\n\n
        • Translated down 2<\/strong> \u2192 subtract 2.<\/li>\n<\/ul>\n\n\n\n

          So:
          f(x)=\u22123×3\u22122f(x) = -3\\sqrt[3]{x} – 2<\/strong><\/p>\n\n\n\n

          \n\n\n\n

          Explanation:<\/strong><\/h3>\n\n\n\n

          This worksheet focuses on identifying and writing transformations of radical functions from their parent functions. The parent functions here are x\\sqrt{x} and x3\\sqrt[3]{x}, representing square root and cube root graphs, respectively.<\/p>\n\n\n\n

          In question 1, the equation f(x)=2x\u22129f(x) = 2\\sqrt{x} – 9 shows a vertical stretch<\/strong> by 2 and a shift downward<\/strong> by 9. This means that every point on the graph is stretched vertically (y-values double) and then moved down.<\/p>\n\n\n\n

          In question 2, f(x)=\u2212x+53+3f(x) = -\\sqrt[3]{x + 5} + 3 applies several transformations: first, a left shift<\/strong> by 5 units because of x+5x + 5, then a reflection over the x-axis<\/strong> (the negative sign flips the graph upside down), followed by a shift upward<\/strong> by 3 units.<\/p>\n\n\n\n

          Question 3 is more involved. We are told the function is a compressed<\/strong> version of x\\sqrt{x} (multiplied by 13\\frac{1}{3}), and it\u2019s translated to end at the point (4, -1). Using the general form of a square root function with transformations, we substitute the point (4, -1) to find the horizontal and vertical shifts.<\/p>\n\n\n\n

          Question 4 describes a cube root function reflected over the x-axis, stretched vertically by a factor of 3, and shifted down by 2. All these transformations are incorporated into the function as: multiply by -3 and subtract 2.<\/p>\n\n\n\n

          Understanding these transformations helps in graphing and interpreting the behavior of radical functions.<\/p>\n\n\n\n

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

          Radical Functions Date: Bell: Homework 7: Graphing Radical Functions This is a 2-page document. ** For questions 1-2: Describe the transformations from the parent function f(x) = \u00e2\u02c6\u0161x. 3. The square root parent function is vertically compressed by a factor of 1\/3, then translated so that it has an endpoint located at (4, -1). Write […]<\/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-225186","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225186","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=225186"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225186\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225186"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}