{"id":270566,"date":"2025-07-25T08:19:58","date_gmt":"2025-07-25T08:19:58","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=270566"},"modified":"2025-07-25T08:20:00","modified_gmt":"2025-07-25T08:20:00","slug":"is-f-2-negative-yes-no","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/25\/is-f-2-negative-yes-no\/","title":{"rendered":"Is\u00a0f(-2)\u00a0 \u00a0negative? Yes No\u00a0"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

The correct answer for part (b) is:
(-4, -1) U (3, \u221e)<\/strong><\/p>\n\n\n\n

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

To find the values of x for which f(x) > 0, we need to determine the intervals where the function’s graph lies above the x-axis. We can deduce this by using the information provided in parts (a) and (c).<\/p>\n\n\n\n

First, let’s look at part (c). It tells us that f(x) = 0 for the x-values -4, -1, and 3. These are the roots, or x-intercepts, of the function. These are the points where the function\u2019s value is neither positive nor negative. These roots divide the number line into four intervals: (-\u221e, -4), (-4, -1), (-1, 3), and (3, \u221e). Within each of these intervals, the sign of f(x) will be consistent, meaning it will be either entirely positive or entirely negative.<\/p>\n\n\n\n

Next, we use the clue from part (a), which states that f(-2) is not negative. Since x = -2 is not one of the roots, f(-2) cannot be zero. This means f(-2) must be positive. The input value x = -2 is located within the interval (-4, -1). Because we have found a point in this interval where the function is positive, we can conclude that f(x) is positive for the entire interval (-4, -1).<\/p>\n\n\n\n

Assuming the function is a continuous polynomial-like curve that crosses the x-axis at each root, the sign of the function will alternate between adjacent intervals. Since the function is positive on (-4, -1), it must be negative on the interval to its right, (-1, 3). Following this alternating pattern, the function must be positive again on the next interval, (3, \u221e). Similarly, it must have been negative on the interval to the left of (-4, -1), which is (-\u221e, -4).<\/p>\n\n\n\n

Therefore, the function f(x) is positive, or f(x) > 0, on the intervals (-4, -1) and (3, \u221e). The question asks for the answer in interval notation, so we combine these two intervals using the union symbol (U).<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: The correct answer for part (b) is:(-4, -1) U (3, \u221e) Explanation To find the values of x for which f(x) > 0, we need to determine the intervals where the function’s graph lies above the x-axis. We can deduce this by using the information provided in parts (a) […]<\/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-270566","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/270566","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=270566"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/270566\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=270566"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=270566"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=270566"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}