Write an equation for the following transformation of y =x; a vertical compression by a factor of 1\/4
a. y=-4x
b. y= -1\/4x
c. y = 4x
d. y = 1\/4x<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is d. y = 1\/4x<\/strong>.<\/p>\n\n\n\n The transformation described in the problem is a vertical compression by a factor of 1\/4<\/strong>. Let’s break down the components to understand how this transformation affects the graph of the function.<\/p>\n\n\n\n Thus, the correct transformation of y = x<\/strong> with a vertical compression by a factor of 1\/4<\/strong> is y = 1\/4x<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Write an equation for the following transformation of y =x; a vertical compression by a factor of 1\/4a. y=-4xb. y= -1\/4xc. y = 4xd. y = 1\/4x The Correct Answer and Explanation is : The correct answer is d. y = 1\/4x. Explanation: The transformation described in the problem is a vertical compression by a […]<\/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-164372","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164372","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=164372"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164372\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=164372"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=164372"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=164372"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
\n
The function given is y = x<\/strong>, which represents a straight line with a slope of 1. In this case, for every increase of 1 unit in x<\/strong>, y<\/strong> increases by 1 unit.<\/li>\n\n\n\n
A vertical compression by a factor of 1\/4<\/strong> means that the graph of the function is “squished” vertically, making it flatter. For each value of x<\/strong>, the corresponding y<\/strong> value is multiplied by 1\/4<\/strong>, meaning the values of y<\/strong> become one-quarter of their original values for any given x<\/strong>.<\/li>\n\n\n\n
To apply a vertical compression by a factor of 1\/4<\/strong>, we multiply the entire function y = x<\/strong> by 1\/4<\/strong>:
[
y = \\frac{1}{4}x
]
This equation represents a line with the same slope as the original line, but the y<\/strong>-values are scaled down by a factor of 1\/4<\/strong>. The line will still pass through the origin, but it will be closer to the x-axis compared to the original line y = x<\/strong>.<\/li>\n\n\n\n\n