The range of which function includes -4? <\/p>\n\n\n\n
y = sqrt(x) – 5 <\/p>\n\n\n\n
y = sqrt(x) + 5 <\/p>\n\n\n\n
y = sqrt(x + 5) <\/p>\n\n\n\n
y = sqrt(x – 5)<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: (y = \\sqrt{x} – 5)<\/strong><\/p>\n\n\n\n To determine which function has a range that includes -4, we need to analyze each function individually, focusing on how the square root function behaves and how it affects the overall expression.<\/p>\n\n\n\n Conclusion:<\/strong> The range of which function includes -4? y = sqrt(x) – 5 y = sqrt(x) + 5 y = sqrt(x + 5) y = sqrt(x – 5) The Correct Answer and Explanation is : The correct answer is: (y = \\sqrt{x} – 5) To determine which function has a range that includes -4, we need […]<\/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-149824","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149824","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=149824"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149824\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=149824"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=149824"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=149824"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
The square root function, (\\sqrt{x}), has a minimum value of 0 (which occurs when (x = 0)). Thus, the minimum value of (y) can be calculated as follows:
[
y_{\\text{min}} = 0 – 5 = -5
]
Since (\\sqrt{x}) can take values starting from 0 and going to positive infinity, (y) can take values from -5 to positive infinity. Therefore, the range is ([-5, \\infty)), which includes -4.<\/li>\n\n\n\n
Here, the minimum value occurs again when (x = 0):
[
y_{\\text{min}} = 0 + 5 = 5
]
The range for this function starts at 5 and goes to positive infinity, represented as ([5, \\infty)). This range does not include -4.<\/li>\n\n\n\n
For this function, the minimum occurs when (x + 5 = 0) (i.e., (x = -5)):
[
y_{\\text{min}} = \\sqrt{0} = 0
]
Thus, the range is ([0, \\infty)), which does not include -4.<\/li>\n\n\n\n
The minimum value for this function occurs when (x – 5 = 0) (i.e., (x = 5)):
[
y_{\\text{min}} = \\sqrt{0} = 0
]
The range is also ([0, \\infty)), which does not include -4.<\/li>\n<\/ol>\n\n\n\n
Among the given functions, the correct answer is (y = \\sqrt{x} – 5)<\/strong>, as its range is ([-5, \\infty)), which includes -4. The other functions do not allow for negative values in their ranges, which disqualifies them from including -4.<\/p>\n","protected":false},"excerpt":{"rendered":"