For what value(s) of k will the relation not be a function?
A = {(1.5k\u22124, 7), (\u22120.5k+8, 15)}<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To determine the value(s) of ( k ) for which the given relation ( A = {(1.5k – 4, 7), (-0.5k + 8, 15)} ) is not a function<\/strong>, we must first recall the definition of a function. A relation is a function if each input<\/strong> (or domain element<\/strong>) corresponds to exactly one output<\/strong> (or range element<\/strong>).<\/p>\n\n\n\n In this case, the relation ( A ) consists of two ordered pairs: ( (1.5k – 4, 7) ) and ( (-0.5k + 8, 15) ). For this to be a function, the first elements<\/strong> (inputs) of the pairs must be distinct. If they are not distinct, the relation will fail to be a function, as it would violate the rule that each input should correspond to only one output.<\/p>\n\n\n\n The inputs of the two ordered pairs are ( 1.5k – 4 ) and ( -0.5k + 8 ). For the relation to not<\/strong> be a function, these two inputs must be equal, as that would imply the same input leads to different outputs, which breaks the definition of a function.<\/p>\n\n\n\n Set the two inputs equal to each other:<\/p>\n\n\n\n [ First, get all the terms involving ( k ) on one side:<\/p>\n\n\n\n [ [ Now, solve for ( k ):<\/p>\n\n\n\n [ For ( k = 6 ), the two inputs become equal, meaning the relation is not a function<\/strong> because the input ( 1.5(6) – 4 = 9 – 4 = 5 ) is the same for both ordered pairs, while the corresponding outputs are different (7 and 15). Therefore, the value of ( k ) that makes the relation not a function is ( k = 6 ).<\/p>\n\n\n\n Thus, the answer is ( k = 6 )<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" For what value(s) of k will the relation not be a function?A = {(1.5k\u22124, 7), (\u22120.5k+8, 15)} The Correct Answer and Explanation is: To determine the value(s) of ( k ) for which the given relation ( A = {(1.5k – 4, 7), (-0.5k + 8, 15)} ) is not a function, we must first […]<\/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-167480","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167480","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=167480"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167480\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167480"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167480"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167480"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Set the inputs equal to each other<\/h3>\n\n\n\n
1.5k – 4 = -0.5k + 8
]<\/p>\n\n\n\nStep 2: Solve for ( k )<\/h3>\n\n\n\n
1.5k + 0.5k = 8 + 4
]<\/p>\n\n\n\n
2k = 12
]<\/p>\n\n\n\n
k = \\frac{12}{2} = 6
]<\/p>\n\n\n\nStep 3: Conclusion<\/h3>\n\n\n\n