{"id":187565,"date":"2025-02-05T05:27:15","date_gmt":"2025-02-05T05:27:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=187565"},"modified":"2025-02-05T05:27:17","modified_gmt":"2025-02-05T05:27:17","slug":"use-the-x-cubed-tool-to-graph-the-x-cubed-function","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/05\/use-the-x-cubed-tool-to-graph-the-x-cubed-function\/","title":{"rendered":"Use the\u200b x-cubed tool to graph the\u200b x-cubed function"},"content":{"rendered":"\n

Use the\u200b x-cubed tool to graph the\u200b x-cubed function. Update the function to have a Vertical Stretch of\u200b 3, a Horizontal Stretch of\u200b 1, a Vertical Shift of\u200b 0, a Horizontal Shift of\u200b 5, and a Reflection over the\u200bx-axis.<\/p>\n\n\n\n

Use the\u200b x-cubed tool button<\/p>\n\n\n\n

on the graphing palette to place the function on the graph. Then update the Vertical\u200b Stretch, Horizontal\u200b Stretch, Vertical\u200b Shift, Horizontal\u200b Shift, and Reflect over\u200b x-axis interactions to have the values noted above.<\/p>\n\n\n\n

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

To graph the transformed cubic function with the given transformations, follow these steps:<\/p>\n\n\n\n

Step 1: Understand the Base Function<\/strong><\/h3>\n\n\n\n

The parent function is:
[
f(x) = x^3
]<\/p>\n\n\n\n

Step 2: Apply Transformations<\/strong><\/h3>\n\n\n\n

We need to apply the following transformations:<\/p>\n\n\n\n

    \n
  1. Vertical Stretch by 3<\/strong>: Multiply the function by 3:
    [
    f(x) = 3x^3
    ]<\/li>\n\n\n\n
  2. Horizontal Stretch by 1<\/strong>: A horizontal stretch by a factor of ( a ) is represented as ( f(x) = (1\/a \\cdot x)^3 ). Since the factor is 1, the function remains unchanged.<\/li>\n\n\n\n
  3. Horizontal Shift by 5<\/strong>: This means shifting the graph to the right by 5 units. Replace ( x ) with ( (x – 5) ):
    [
    f(x) = 3(x – 5)^3
    ]<\/li>\n\n\n\n
  4. Vertical Shift of 0<\/strong>: Since there’s no vertical shift, the function remains the same.<\/li>\n\n\n\n
  5. Reflection over the x-axis<\/strong>: To reflect over the x-axis, multiply the entire function by ( -1 ):
    [
    f(x) = -3(x – 5)^3
    ]<\/li>\n<\/ol>\n\n\n\n

    Step 3: Final Transformed Function<\/strong><\/h3>\n\n\n\n

    [
    f(x) = -3(x – 5)^3
    ]<\/p>\n\n\n\n

    Explanation of Transformations<\/strong><\/h3>\n\n\n\n
      \n
    • The vertical stretch by 3<\/strong> makes the graph steeper, meaning it grows faster in magnitude.<\/li>\n\n\n\n
    • The horizontal stretch of 1<\/strong> keeps the function’s width unchanged.<\/li>\n\n\n\n
    • The horizontal shift of 5<\/strong> moves the function 5 units to the right.<\/li>\n\n\n\n
    • The vertical shift of 0<\/strong> means there is no movement up or down.<\/li>\n\n\n\n
    • The reflection over the x-axis<\/strong> flips the function upside down, making all positive y-values negative and vice versa.<\/li>\n<\/ul>\n\n\n\n

      Graphing Instructions<\/strong><\/h3>\n\n\n\n
        \n
      1. Plot the parent function ( x^3 ).<\/li>\n\n\n\n
      2. Shift it 5 units right<\/strong>.<\/li>\n\n\n\n
      3. Apply a vertical stretch<\/strong> by multiplying y-values by 3.<\/li>\n\n\n\n
      4. Reflect the graph over the x-axis.<\/li>\n\n\n\n
      5. The final function should pass through (5,0) and follow the transformed cubic shape.<\/li>\n<\/ol>\n\n\n\n

        Now, let’s generate a graph of this function.<\/p>\n\n\n\n

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

        Here is the graph of the function ( f(x) = -3(x – 5)^3 ). The key transformations are applied:<\/p>\n\n\n\n

          \n
        • Shifted 5 units to the right<\/strong>, moving the inflection point from (0,0) to (5,0).<\/li>\n\n\n\n
        • Vertically stretched by 3<\/strong>, making the curve steeper.<\/li>\n\n\n\n
        • Reflected over the x-axis<\/strong>, flipping the original cubic shape upside down.<\/li>\n<\/ul>\n\n\n\n

          This visualization confirms how the transformations affect the parent function. Let me know if you need further clarification! \ud83d\ude80<\/p>\n","protected":false},"excerpt":{"rendered":"

          Use the\u200b x-cubed tool to graph the\u200b x-cubed function. Update the function to have a Vertical Stretch of\u200b 3, a Horizontal Stretch of\u200b 1, a Vertical Shift of\u200b 0, a Horizontal Shift of\u200b 5, and a Reflection over the\u200bx-axis. Use the\u200b x-cubed tool button on the graphing palette to place the function on the graph. […]<\/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-187565","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187565","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=187565"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187565\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187565"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187565"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187565"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}