f(x) = x + 5 + 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 8 units down. Write an equation that could represent this function.<\/p>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/image-508.png\")
<\/figure>\n\n\n\nThe Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n Given: Transformations from the parent function<\/strong> f(x)=x3f(x) = \\sqrt[3]{x}:<\/p>\n\n\n\n \u2705 Final answer for #2<\/strong>:<\/p>\n\n\n\n We are asked to write an equation for the cube root parent function, given these transformations:<\/p>\n\n\n\n Start with the parent function<\/strong>: Apply transformations<\/strong>:<\/p>\n\n\n\n \u2705 Final equation for #4<\/strong>: Transformations of functions involve shifting, stretching, compressing, or reflecting the graph of a parent function. Understanding how each change affects the graph helps us write or interpret equations correctly.<\/p>\n\n\n\n For question #2<\/strong>, we start with the cube root parent function<\/strong> f(x)=x3f(x) = \\sqrt[3]{x}. The term x+5x + 5 inside the radical shifts the graph left by 5 units<\/strong>, because the inside of the function affects the horizontal<\/strong> position in the opposite<\/strong> direction. The negative sign in front<\/strong> reflects the graph over the x-axis<\/strong>, flipping it upside down. Finally, adding 3 outside the function shifts the graph up by 3 units<\/strong>, moving every point vertically.<\/p>\n\n\n\n For question #4<\/strong>, we apply a sequence of transformations<\/strong> starting with the parent cube root function. Reflecting over the x-axis changes the sign of the function, so x3\\sqrt[3]{x} becomes \u2212x3-\\sqrt[3]{x}. Then, stretching the function vertically by a factor of 3 means that all y-values are three times farther from the x-axis, changing it to \u22123×3-3\\sqrt[3]{x}. Lastly, subtracting 8 translates the function downward<\/strong> by 8 units. So the full equation becomes f(x)=\u22123×3\u22128f(x) = -3\\sqrt[3]{x} – 8.<\/p>\n\n\n\n These types of transformations help students understand how different algebraic modifications affect a function\u2019s graph and behavior.<\/p>\n\n\n\n Name: Unit 6: Radical Functions Homework Date: Bell: This is a 2-page document. For questions 1-2: Describe the transformations from the parent function. S(x) = -2x – 9f(x) = x + 5 + 3The square root parent function is vertically compressed by a factor of 1\/3, then translated so that it has an endpoint located […]<\/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-221031","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221031","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=221031"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221031\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=221031"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=221031"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=221031"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nQuestion 2:<\/strong><\/h3>\n\n\n\n
f(x)=\u2212x+53+3f(x) = -\\sqrt[3]{x+5} + 3<\/p>\n\n\n\n\n
\u2192 This is a horizontal shift 5 units to the left<\/strong>.<\/li>\n\n\n\n
\u2192 This is a reflection across the x-axis<\/strong>.<\/li>\n\n\n\n
\u2192 This is a vertical shift 3 units up<\/strong>.<\/li>\n<\/ol>\n\n\n\n\n
\n\n\n\nQuestion 4:<\/strong><\/h3>\n\n\n\n
\n
f(x)=x3f(x) = \\sqrt[3]{x}<\/p>\n\n\n\n\n
f(x)=\u2212x3f(x) = -\\sqrt[3]{x}<\/li>\n\n\n\n
f(x)=\u22123x3f(x) = -3\\sqrt[3]{x}<\/li>\n\n\n\n
f(x)=\u22123×3\u22128f(x) = -3\\sqrt[3]{x} – 8<\/li>\n<\/ol>\n\n\n\n
f(x)=\u22123×3\u22128f(x) = -3\\sqrt[3]{x} – 8<\/strong><\/p>\n\n\n\n
\n\n\n\nExplanation <\/strong><\/h3>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/learnexams-banner4-92.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"