{"id":157695,"date":"2024-10-22T19:13:51","date_gmt":"2024-10-22T19:13:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=157695"},"modified":"2024-10-22T19:13:53","modified_gmt":"2024-10-22T19:13:53","slug":"consider-the-function-fx56x2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/22\/consider-the-function-fx56x2\/","title":{"rendered":"Consider the function f(x)=56&#215;2."},"content":{"rendered":"\n<p>Consider the function f(x)=56&#215;2. Part A<br>What type of function does the equation model?<br>A. Linear<br>B. Quadratic<br>C. Exponential<br>D. Absolute value<br>Part B<\/p>\n\n\n\n<p>What is the value of the function when x = 12?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To analyze the function ( f(x) = 56x^2 ), we will go through each part of your question.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part A: Type of Function<\/h3>\n\n\n\n<p>The function ( f(x) = 56x^2 ) is a <strong>quadratic function<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Linear Functions<\/strong> are characterized by a constant rate of change and can be represented in the form ( f(x) = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. Linear functions produce a straight line when graphed.<\/li>\n\n\n\n<li><strong>Quadratic Functions<\/strong>, like our given function, have the general form ( f(x) = ax^2 + bx + c ) where ( a ), ( b ), and ( c ) are constants, and ( a \\neq 0 ). The presence of the ( x^2 ) term indicates that the function will produce a parabolic shape when graphed. In this case, ( a = 56 ) is a positive constant, which means the parabola opens upwards.<\/li>\n\n\n\n<li><strong>Exponential Functions<\/strong> can be expressed in the form ( f(x) = a \\cdot b^x ), where ( a ) is a constant, and ( b ) is the base of the exponent. These functions grow much faster than quadratic functions.<\/li>\n\n\n\n<li><strong>Absolute Value Functions<\/strong> are represented as ( f(x) = |x| ) and display a distinct V-shape on a graph, with the output being always non-negative.<\/li>\n<\/ul>\n\n\n\n<p>Given that ( f(x) = 56x^2 ) contains the term ( x^2 ) and matches the form of a quadratic function, the correct answer is <strong>B. Quadratic<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part B: Value of the Function at ( x = 12 )<\/h3>\n\n\n\n<p>To find the value of the function when ( x = 12 ), we substitute ( x ) into the function:<\/p>\n\n\n\n<p>[<br>f(12) = 56(12^2)<br>]<\/p>\n\n\n\n<p>Calculating ( 12^2 ):<\/p>\n\n\n\n<p>[<br>12^2 = 144<br>]<\/p>\n\n\n\n<p>Now substitute ( 144 ) back into the function:<\/p>\n\n\n\n<p>[<br>f(12) = 56 \\cdot 144<br>]<\/p>\n\n\n\n<p>To perform this multiplication:<\/p>\n\n\n\n<p>[<br>56 \\cdot 144 = 8064<br>]<\/p>\n\n\n\n<p>Thus, the value of the function at ( x = 12 ) is:<\/p>\n\n\n\n<p>[<br>\\boxed{8064}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>The evaluation of ( f(12) ) demonstrates how quadratic functions behave as the input values increase. As seen in the calculations, the output grows significantly as ( x ) becomes larger. This characteristic highlights the non-linear growth of quadratic functions compared to linear functions. Quadratics can model various real-world phenomena where acceleration or growth is involved, such as projectile motion or certain financial calculations. The ( x^2 ) term leads to exponential-like increases in values as ( x ) rises, which is evident in our calculation where ( f(12) ) yields 8064. Such functions are crucial in fields like physics, engineering, and economics, providing insights into relationships involving squared terms, thus validating their application in real-world scenarios.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider the function f(x)=56&#215;2. Part AWhat type of function does the equation model?A. LinearB. QuadraticC. ExponentialD. Absolute valuePart B What is the value of the function when x = 12? The Correct Answer and Explanation is: To analyze the function ( f(x) = 56x^2 ), we will go through each part of your question. Part [&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-157695","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157695","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=157695"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157695\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=157695"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=157695"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=157695"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}