{"id":164546,"date":"2024-11-10T10:35:34","date_gmt":"2024-11-10T10:35:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=164546"},"modified":"2024-11-10T10:35:36","modified_gmt":"2024-11-10T10:35:36","slug":"what-form-of-correspondence-does-the-function-fx-2x-5-have","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/10\/what-form-of-correspondence-does-the-function-fx-2x-5-have\/","title":{"rendered":"What form of correspondence does the function f(x) = 2x + 5 have"},"content":{"rendered":"\n<p>What form of correspondence does the function f(x) = 2x + 5 have?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The function ( f(x) = 2x + 5 ) is an <strong>linear function<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>A <strong>linear function<\/strong> is a type of function where the highest degree of the variable ( x ) is 1. The general form of a linear function is given by:<\/p>\n\n\n\n<p>[<br>f(x) = mx + b<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( m ) is the slope of the line, and<\/li>\n\n\n\n<li>( b ) is the y-intercept, or the point where the line crosses the y-axis.<\/li>\n<\/ul>\n\n\n\n<p>In the function ( f(x) = 2x + 5 ):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The slope ( m ) is 2. This means for every 1 unit increase in ( x ), ( f(x) ) (or ( y )) increases by 2 units.<\/li>\n\n\n\n<li>The y-intercept ( b ) is 5, indicating that the line crosses the y-axis at ( y = 5 ) (when ( x = 0 )).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Graphical Representation:<\/h3>\n\n\n\n<p>The graph of a linear function is always a straight line. For ( f(x) = 2x + 5 ), the line will have a slope of 2 and will pass through the point ( (0, 5) ) on the y-axis. The line extends infinitely in both directions, maintaining a constant slope.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Properties of Linear Functions:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Constant rate of change<\/strong>: The slope ( m ) represents the constant rate of change between ( x ) and ( f(x) ). In this case, for every unit increase in ( x ), the value of ( f(x) ) increases by 2 units.<\/li>\n\n\n\n<li><strong>Straight line<\/strong>: Since the function is linear, its graph is a straight line, with no curves or bends.<\/li>\n\n\n\n<li><strong>No exponents higher than 1<\/strong>: The variable ( x ) only has an exponent of 1, which is characteristic of a linear function. Functions with exponents greater than 1 are called polynomial functions of higher degree (quadratic, cubic, etc.).<\/li>\n<\/ol>\n\n\n\n<p>Thus, ( f(x) = 2x + 5 ) is a linear function with a slope of 2 and a y-intercept of 5.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What form of correspondence does the function f(x) = 2x + 5 have? The Correct Answer and Explanation is : The function ( f(x) = 2x + 5 ) is an linear function. Explanation: A linear function is a type of function where the highest degree of the variable ( x ) is 1. The [&hellip;]<\/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-164546","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164546","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=164546"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164546\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=164546"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=164546"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=164546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}