{"id":186879,"date":"2025-01-26T10:28:10","date_gmt":"2025-01-26T10:28:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186879"},"modified":"2025-01-26T10:28:12","modified_gmt":"2025-01-26T10:28:12","slug":"write-the-function-for-sx-if-the-absolute-value-parent-function-fx-lx-is-reflected-across-the-x-axis","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/26\/write-the-function-for-sx-if-the-absolute-value-parent-function-fx-lx-is-reflected-across-the-x-axis\/","title":{"rendered":"Write The Function For S(X) If The Absolute Value Parent Function F(X)- Lx Is Reflected Across The X-Axis"},"content":{"rendered":"\n

Write The Function For S(X) If The Absolute Value Parent Function F(X)- Lx Is Reflected Across The X-Axis, Horizontally Stretched By A Factor Of 4, And Then Translated Horizontally 3 Units Right And Vertically 7 Units Up. Function: F(X)=4] X- +1<\/p>\n\n\n\n

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

To derive the function ( S(x) ) from the absolute value parent function ( F(x) = |x| ), we will apply the specified transformations step by step:<\/p>\n\n\n\n

    \n
  1. Reflection Across the X-Axis<\/strong>: Reflecting ( F(x) = |x| ) across the x-axis changes the function to ( -|x| ). This transformation inverts the graph, flipping it upside down.<\/li>\n\n\n\n
  2. Horizontal Stretch by a Factor of 4<\/strong>: To horizontally stretch the function by a factor of 4, we replace ( x ) with ( \\frac{x}{4} ). This results in the function ( -\\left| \\frac{x}{4} \\right| ). Horizontal stretches affect the x-values, making the graph wider.<\/li>\n\n\n\n
  3. Translation 3 Units to the Right<\/strong>: Translating the function 3 units to the right involves replacing ( x ) with ( x – 3 ). The function becomes ( -\\left| \\frac{x – 3}{4} \\right| ). Horizontal translations shift the graph along the x-axis.<\/li>\n\n\n\n
  4. Translation 7 Units Up<\/strong>: Finally, translating the function 7 units up adds 7 to the entire expression, resulting in ( S(x) = -\\left| \\frac{x – 3}{4} \\right| + 7 ). Vertical translations move the graph along the y-axis.<\/li>\n<\/ol>\n\n\n\n

    Thus, the transformed function is:<\/p>\n\n\n\n

    [ S(x) = -\\left| \\frac{x – 3}{4} \\right| + 7 ]<\/p>\n\n\n\n

    Explanation of Transformations<\/strong>:<\/p>\n\n\n\n

      \n
    • Reflection Across the X-Axis<\/strong>: Reflecting a function across the x-axis changes the sign of all its output values. For the absolute value function ( F(x) = |x| ), this reflection results in ( -|x| ), flipping the graph upside down.<\/li>\n\n\n\n
    • Horizontal Stretch by a Factor of 4<\/strong>: A horizontal stretch by a factor of 4 means that for every x-value, the corresponding y-value remains the same, but the graph becomes wider. This is achieved by replacing ( x ) with ( \\frac{x}{4} ), which scales the x-values by a factor of 4.<\/li>\n\n\n\n
    • Translation 3 Units to the Right<\/strong>: Translating a function to the right by 3 units involves replacing ( x ) with ( x – 3 ). This shifts the entire graph 3 units along the x-axis, moving all points to the right.<\/li>\n\n\n\n
    • Translation 7 Units Up<\/strong>: Translating a function upward by 7 units adds 7 to the entire function. This shifts the graph 7 units along the y-axis, moving all points up.<\/li>\n<\/ul>\n\n\n\n

      By applying these transformations in sequence, we obtain the final function ( S(x) = -\\left| \\frac{x – 3}{4} \\right| + 7 ), which represents the absolute value parent function reflected across the x-axis, horizontally stretched by a factor of 4, and translated 3 units to the right and 7 units up.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Write The Function For S(X) If The Absolute Value Parent Function F(X)- Lx Is Reflected Across The X-Axis, Horizontally Stretched By A Factor Of 4, And Then Translated Horizontally 3 Units Right And Vertically 7 Units Up. Function: F(X)=4] X- +1 The Correct Answer and Explanation is : To derive the function ( S(x) ) […]<\/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-186879","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186879","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=186879"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186879\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186879"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186879"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186879"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}