{"id":160381,"date":"2024-11-02T19:45:25","date_gmt":"2024-11-02T19:45:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=160381"},"modified":"2024-11-02T19:45:26","modified_gmt":"2024-11-02T19:45:26","slug":"which-function-is-graphed-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/02\/which-function-is-graphed-below\/","title":{"rendered":"Which function is graphed below"},"content":{"rendered":"\n

Which function is graphed below?
On a coordinate plane, a curve goes through (0, 0), has a maximum point at 1, and has a minimum point at -1. It increases through (0, 0). A. f(x)=\u2212cos(x) B. f(x)=cos(x) C. f(x)=sin(x) D. f(x)=\u2212sin(x)<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The function that best describes the curve graphed in the description is D. f(x) = -sin(x)<\/strong>.<\/p>\n\n\n\n

To understand why this is the correct choice, we need to analyze the properties of the sine function and how the negative transformation affects its graph. The function (f(x) = \\sin(x)) oscillates between -1 and 1, with the following characteristics:<\/p>\n\n\n\n

    \n
  1. Behavior of the Sine Function<\/strong>: The standard sine function, (f(x) = \\sin(x)), starts at (0, 0) and rises to a maximum of 1 at (x = \\frac{\\pi}{2}) before descending back to 0 at (x = \\pi). It has a minimum point of -1 at (x = \\frac{3\\pi}{2}).<\/li>\n\n\n\n
  2. Effect of Negation<\/strong>: When we consider the function (f(x) = -\\sin(x)), we essentially reflect the sine curve across the x-axis. This transformation alters the behavior significantly: the function now starts at (0, 0) and initially decreases to a minimum of -1 at (x = \\frac{\\pi}{2}) before returning to 0 at (x = \\pi), and then it increases to a maximum of 1 at (x = \\frac{3\\pi}{2}).<\/li>\n\n\n\n
  3. Maximum and Minimum Points<\/strong>: Given the description in the problem, the function passes through (0, 0), achieves a maximum point at (1, 0), and a minimum at (-1, 0). The characteristics of the graph described\u2014having a maximum at (y = 1) and a minimum at (y = -1)\u2014fit perfectly with the behavior of (f(x) = -\\sin(x)).<\/li>\n<\/ol>\n\n\n\n

    In conclusion, based on the given features\u2014starting point, maximum and minimum points, and the general behavior of the sine function under negation\u2014the graph corresponds to the function D. f(x) = -sin(x)<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Which function is graphed below?On a coordinate plane, a curve goes through (0, 0), has a maximum point at 1, and has a minimum point at -1. It increases through (0, 0). A. f(x)=\u2212cos(x) B. f(x)=cos(x) C. f(x)=sin(x) D. f(x)=\u2212sin(x) The Correct Answer and Explanation is: The function that best describes the curve graphed in […]<\/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-160381","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160381","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=160381"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160381\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=160381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=160381"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=160381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}