{"id":226032,"date":"2025-06-04T20:08:33","date_gmt":"2025-06-04T20:08:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226032"},"modified":"2025-06-04T20:08:35","modified_gmt":"2025-06-04T20:08:35","slug":"points-which-of-the-following-best-describes-the-graph-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/points-which-of-the-following-best-describes-the-graph-below\/","title":{"rendered":"Points Which of the following best describes the graph below"},"content":{"rendered":"\n

Points Which of the following best describes the graph below? +3 +2 +1 5 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 A. It is not a function. B. It is a many-to-one function. C. It is a function, but it is not one-to-one. D. It is a one-to-one function. ? PREVIOUS<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

The correct answer is: D. It is a one-to-one function.<\/strong><\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

To analyze the given graph, we first determine if the red curve represents a function. A graph represents a function if it passes the vertical line test<\/strong>\u2014that is, no vertical line should intersect the graph at more than one point. This condition ensures that each input (x-value) corresponds to exactly one output (y-value).<\/p>\n\n\n\n

Looking at the graph, each vertical line would intersect the curve at only one point<\/strong>. Therefore, it is<\/strong> a function.<\/p>\n\n\n\n

Next, we examine whether it is a one-to-one<\/strong> function. A function is one-to-one if it also passes the horizontal line test<\/strong>\u2014meaning no horizontal line intersects the graph more than once. This guarantees that each output (y-value) is mapped from exactly one input (x-value), which means the function is injective.<\/p>\n\n\n\n

From the graph provided, any horizontal line would also intersect the curve at most once. This means that no two different x-values produce the same y-value. Hence, the function passes both the vertical and horizontal line tests.<\/p>\n\n\n\n

This confirms the function is one-to-one<\/strong> (injective) and well-defined<\/strong> (it assigns exactly one output to each input).<\/p>\n\n\n\n

Let’s briefly address the other answer choices to show why they are incorrect:<\/p>\n\n\n\n

    \n
  • A. It is not a function<\/strong> \u2013 Incorrect, because it passes the vertical line test.<\/li>\n\n\n\n
  • B. It is a many-to-one function<\/strong> \u2013 Incorrect, since each output is matched with only one input, not multiple.<\/li>\n\n\n\n
  • C. It is a function, but it is not one-to-one<\/strong> \u2013 Incorrect, because the function is<\/em> one-to-one as it passes the horizontal line test.<\/li>\n\n\n\n
  • D. It is a one-to-one function<\/strong> \u2013 Correct<\/strong>, for the reasons described above.<\/li>\n<\/ul>\n\n\n\n

    Thus, the graph best describes a one-to-one function<\/strong>.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Points Which of the following best describes the graph below? +3 +2 +1 5 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 A. It is not a function. B. It is a many-to-one function. C. It is a function, but it is not one-to-one. D. It is a one-to-one function. ? […]<\/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-226032","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226032","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=226032"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226032\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226032"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226032"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226032"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}