{"id":170742,"date":"2024-11-19T22:53:39","date_gmt":"2024-11-19T22:53:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=170742"},"modified":"2024-11-19T22:53:41","modified_gmt":"2024-11-19T22:53:41","slug":"if-you-horizontally-stretch-the-square-root-parent-function-fx-%e2%88%9a%e2%88%9ax-by-%c2%b3-units-what-is-the-equation-of-the-new-function","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/if-you-horizontally-stretch-the-square-root-parent-function-fx-%e2%88%9a%e2%88%9ax-by-%c2%b3-units-what-is-the-equation-of-the-new-function\/","title":{"rendered":"If you horizontally stretch the square root parent function, F(x) = \u221a\u221ax, by \u00b3\/ units, what is the equation of the new function"},"content":{"rendered":"\n

If you horizontally stretch the square root parent function, F(x) = \u221a\u221ax, by \u00b3\/ units, what is the equation of the new function?
A. G(X) = \u221a\u221ax+3
B. G(x) =
C. G(x) = \u00b3\u221ax
D. G(x)=\u221ax+44<\/p>\n\n\n\n

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

The problem asks about the transformation of the square root function ( f(x) = \\sqrt{x} ) through a horizontal stretch by a factor of ( \\frac{3}{2} ).<\/p>\n\n\n\n

Understanding the Transformation<\/h3>\n\n\n\n

To address the question, we need to understand how a horizontal stretch affects a function. A horizontal stretch<\/strong> by a factor of ( c ) is achieved by replacing ( x ) with ( \\frac{x}{c} ) in the function\u2019s equation. This transformation causes the graph to stretch away from the y-axis, making it “wider.”<\/p>\n\n\n\n

For example, if you stretch the basic square root function ( f(x) = \\sqrt{x} ) horizontally by a factor of ( \\frac{3}{2} ), you replace ( x ) with ( \\frac{x}{\\frac{3}{2}} ), or equivalently ( \\frac{2}{3}x ).<\/p>\n\n\n\n

Transformation of ( f(x) = \\sqrt{x} )<\/h3>\n\n\n\n

The original function is ( f(x) = \\sqrt{x} ). A horizontal stretch by a factor of ( \\frac{3}{2} ) means we replace ( x ) with ( \\frac{2}{3}x ). The new function will be:<\/p>\n\n\n\n

[
g(x) = \\sqrt{\\frac{2}{3}x}
]<\/p>\n\n\n\n

This transformation makes the graph of the function ( f(x) ) wider, stretching it along the x-axis by a factor of ( \\frac{3}{2} ).<\/p>\n\n\n\n

Analyzing the Choices<\/h3>\n\n\n\n

Now, let’s look at the given options and analyze which one matches the transformed function:<\/p>\n\n\n\n

    \n
  • A. ( G(x) = \\sqrt{x+3} )<\/strong>: This is a horizontal shift<\/strong> (right by 3 units), not a stretch.<\/li>\n\n\n\n
  • B. ( G(x) = )<\/strong>: This is incomplete and cannot be correct.<\/li>\n\n\n\n
  • C. ( G(x) = \\sqrt[3]{x} )<\/strong>: This represents a cubic root function, not a square root function, so it is not the correct transformation.<\/li>\n\n\n\n
  • D. ( G(x) = \\sqrt{x} + 44 )<\/strong>: This represents a vertical shift<\/strong> (up by 44 units), not a horizontal stretch.<\/li>\n<\/ul>\n\n\n\n

    Conclusion<\/h3>\n\n\n\n

    None of the provided answers exactly match the horizontal stretch by a factor of ( \\frac{3}{2} ). However, based on the given options, none would correctly reflect the transformation as described (i.e., the answer should be ( G(x) = \\sqrt{\\frac{2}{3}x} )). The correct transformation, if given as an option, would look something like:<\/p>\n\n\n\n

    [
    G(x) = \\sqrt{\\frac{2}{3}x}
    ]<\/p>\n\n\n\n

    Thus, based on the given options, we must conclude that none<\/strong> of them represent the correct transformation, but the equation should have been ( G(x) = \\sqrt{\\frac{2}{3}x} ).<\/p>\n","protected":false},"excerpt":{"rendered":"

    If you horizontally stretch the square root parent function, F(x) = \u221a\u221ax, by \u00b3\/ units, what is the equation of the new function?A. G(X) = \u221a\u221ax+3B. G(x) =C. G(x) = \u00b3\u221axD. G(x)=\u221ax+44 The Correct Answer and Explanation is: The problem asks about the transformation of the square root function ( f(x) = \\sqrt{x} ) through […]<\/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-170742","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170742","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=170742"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170742\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=170742"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=170742"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=170742"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}