{"id":226612,"date":"2025-06-05T12:02:27","date_gmt":"2025-06-05T12:02:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226612"},"modified":"2025-06-05T12:02:29","modified_gmt":"2025-06-05T12:02:29","slug":"which-of-the-following-graphs-could-represent-a-quartic-function","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/05\/which-of-the-following-graphs-could-represent-a-quartic-function\/","title":{"rendered":"Which of the following graphs could represent a quartic function"},"content":{"rendered":"\n

Which of the following graphs could represent a quartic function? A. B. C. D. A. Graph A B. Graph B C. Graph C D. Graph D<\/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: C. Graph C<\/strong><\/p>\n\n\n\n

Explanation (300 words):<\/h3>\n\n\n\n

A quartic function<\/strong> is a polynomial function of degree 4. It has the general form: f(x)=ax4+bx3+cx2+dx+ef(x) = ax^4 + bx^3 + cx^2 + dx + e<\/p>\n\n\n\n

Key characteristics of quartic functions include:<\/p>\n\n\n\n

    \n
  1. Degree 4 Behavior<\/strong>: Since the degree is even, the ends of the graph (as x\u2192\u00b1\u221ex \\to \\pm \\infty) either both rise (if the leading coefficient a>0a > 0) or both fall (if a<0a < 0). This is known as having the same end behavior<\/strong> on both sides.<\/li>\n\n\n\n
  2. Turning Points<\/strong>: A quartic function can have up to 3 turning points<\/strong> (local minima or maxima) and up to 4 real roots<\/strong> (x-intercepts), depending on its coefficients.<\/li>\n<\/ol>\n\n\n\n

    Now, let’s analyze each graph:<\/p>\n\n\n\n

      \n
    • Graph A<\/strong>: This graph has two turning points and opposite end behavior. One end goes up and the other goes down. This indicates an odd-degree<\/strong> polynomial, likely cubic, not quartic.<\/li>\n\n\n\n
    • Graph B<\/strong>: This is a straight line with no curves, which means it\u2019s a linear function<\/strong> (degree 1), not quartic.<\/li>\n\n\n\n
    • Graph C<\/strong>: This graph has three turning points<\/strong> and ends that both go upward<\/strong>, matching the behavior of a quartic function with a positive leading coefficient. It\u2019s the only one that fits both the number of turning points and the same-direction end behavior.<\/li>\n\n\n\n
    • Graph D<\/strong>: While it appears more complex, it has too many turns<\/strong> for a quartic function\u2014likely representing a higher-degree polynomial, such as degree 5 or more. It doesn\u2019t match the behavior expected of a degree-4 polynomial.<\/li>\n<\/ul>\n\n\n\n

      Thus, Graph C<\/strong> is the only one consistent with a quartic function\u2019s characteristics, making it the correct answer.<\/p>\n\n\n\n

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

      Which of the following graphs could represent a quartic function? A. B. C. D. A. Graph A B. Graph B C. Graph C D. Graph D The Correct Answer and Explanation is: The correct answer is: C. Graph C Explanation (300 words): A quartic function is a polynomial function of degree 4. It has the […]<\/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-226612","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226612","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=226612"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226612\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226612"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}