{"id":228436,"date":"2025-06-07T09:38:22","date_gmt":"2025-06-07T09:38:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228436"},"modified":"2025-06-07T09:38:24","modified_gmt":"2025-06-07T09:38:24","slug":"which-of-the-following-functions-illustrates-a-change-in-amplitude","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/which-of-the-following-functions-illustrates-a-change-in-amplitude\/","title":{"rendered":"Which of the following functions illustrates a change in amplitude"},"content":{"rendered":"\n<p>Which of the following functions illustrates a change in amplitude? A. y = 3cos(4x) B. y = 1 + sin(x) C. y = -2 &#8211; cos(x &#8211; \u00cf\u20ac) D. y = tan(2x)<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>In trigonometric functions, <strong>amplitude<\/strong> refers to the maximum vertical distance from the midline (or equilibrium) of the graph to its peak or trough. For <strong>sine and cosine functions<\/strong>, the general form is:y=A\u22c5sin\u2061(Bx+C)+Dory=A\u22c5cos\u2061(Bx+C)+Dy = A \\cdot \\sin(Bx + C) + D \\quad \\text{or} \\quad y = A \\cdot \\cos(Bx + C) + Dy=A\u22c5sin(Bx+C)+Dory=A\u22c5cos(Bx+C)+D<\/p>\n\n\n\n<p>Here, <strong>|A|<\/strong> represents the <strong>amplitude<\/strong> of the wave. If <strong>A = 1<\/strong>, the function oscillates between -1 and 1. If <strong>A = 3<\/strong>, the function stretches vertically to oscillate between -3 and 3.<\/p>\n\n\n\n<p>Let\u2019s examine each option:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A. y = 3cos(4x)<\/strong><br>This function has <strong>A = 3<\/strong>, so the amplitude is 3. This means the graph is a vertically stretched cosine wave compared to the standard <strong>cos(x)<\/strong>, which has an amplitude of 1.<br>\u2705 <strong>This function shows a change in amplitude.<\/strong><\/li>\n\n\n\n<li><strong>B. y = 1 + sin(x)<\/strong><br>This is a vertical <strong>translation<\/strong> of the sine wave. The graph is shifted up by 1 unit, but the amplitude remains 1.<br>\u274c <strong>No change in amplitude.<\/strong><\/li>\n\n\n\n<li><strong>C. y = -2 &#8211; cos(x &#8211; \u03c0)<\/strong><br>This function has a vertical reflection and downward shift, but the amplitude is determined by the coefficient of cosine, which is still 1 (since there\u2019s no number multiplied directly with cos). The &#8220;-2&#8221; is a vertical translation.<br>\u274c <strong>No change in amplitude.<\/strong><\/li>\n\n\n\n<li><strong>D. y = tan(2x)<\/strong><br>The tangent function does <strong>not have an amplitude<\/strong> because it is unbounded \u2014 its values go to positive and negative infinity.<br>\u274c <strong>Amplitude is not defined for tangent.<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Conclusion:<\/strong> Only option <strong>A<\/strong> shows a change in amplitude due to the coefficient <strong>3<\/strong> multiplying the cosine function.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-140.jpeg\" alt=\"\" class=\"wp-image-228437\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which of the following functions illustrates a change in amplitude? A. y = 3cos(4x) B. y = 1 + sin(x) C. y = -2 &#8211; cos(x &#8211; \u00cf\u20ac) D. y = tan(2x) The Correct Answer and Explanation is: Explanation In trigonometric functions, amplitude refers to the maximum vertical distance from the midline (or equilibrium) of [&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-228436","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228436","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=228436"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228436\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228436"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228436"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228436"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}