{"id":242167,"date":"2025-07-04T06:19:22","date_gmt":"2025-07-04T06:19:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=242167"},"modified":"2025-07-04T06:19:31","modified_gmt":"2025-07-04T06:19:31","slug":"what-is-the-domain-and-range-of-y5-tan-x","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/what-is-the-domain-and-range-of-y5-tan-x\/","title":{"rendered":"What is the domain and range of y=5 tan x"},"content":{"rendered":"\n<p>What is the domain and range of y=5 tan x<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The function given is y=5tan\u2061(x)y = 5 \\tan(x), which is a transformation of the basic tangent function y=tan\u2061(x)y = \\tan(x).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Domain:<\/h3>\n\n\n\n<p>The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. The tangent function tan\u2061(x)\\tan(x) is undefined wherever its argument equals an odd multiple of \u03c02\\frac{\\pi}{2}, since the tangent function has vertical asymptotes at these points. Specifically, tan\u2061(x)\\tan(x) is undefined at x=\u03c02+n\u03c0x = \\frac{\\pi}{2} + n\\pi, where nn is any integer.<\/p>\n\n\n\n<p>Since the transformation y=5tan\u2061(x)y = 5 \\tan(x) only affects the vertical stretching of the graph and does not change the points where the function is undefined, the domain of y=5tan\u2061(x)y = 5 \\tan(x) remains the same as that of tan\u2061(x)\\tan(x).<\/p>\n\n\n\n<p>Thus, the domain of y=5tan\u2061(x)y = 5 \\tan(x) is: x\u2208Rexceptx=\u03c02+n\u03c0forn\u2208Zx \\in \\mathbb{R} \\quad \\text{except} \\quad x = \\frac{\\pi}{2} + n\\pi \\quad \\text{for} \\quad n \\in \\mathbb{Z}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Range:<\/h3>\n\n\n\n<p>The range of a function refers to the set of all possible output values (y-values) that the function can take. The tangent function tan\u2061(x)\\tan(x) has a range of all real numbers, i.e., (\u2212\u221e,\u221e)(-\\infty, \\infty). The transformation y=5tan\u2061(x)y = 5 \\tan(x) results in a vertical stretch by a factor of 5, meaning that for every output value of tan\u2061(x)\\tan(x), the corresponding output value of y=5tan\u2061(x)y = 5 \\tan(x) is 5 times greater.<\/p>\n\n\n\n<p>Since the tangent function itself can take any real value, multiplying the output by 5 does not change the fact that the range of y=5tan\u2061(x)y = 5 \\tan(x) is still all real numbers.<\/p>\n\n\n\n<p>Thus, the range of y=5tan\u2061(x)y = 5 \\tan(x) is: y\u2208Ry \\in \\mathbb{R}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Domain: x\u2208Rx \\in \\mathbb{R} except x=\u03c02+n\u03c0x = \\frac{\\pi}{2} + n\\pi, where nn is any integer.<\/li>\n\n\n\n<li>Range: y\u2208Ry \\in \\mathbb{R}.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>What is the domain and range of y=5 tan x The correct answer and explanation is: The function given is y=5tan\u2061(x)y = 5 \\tan(x), which is a transformation of the basic tangent function y=tan\u2061(x)y = \\tan(x). Domain: The domain of a function refers to the set of all possible input values (x-values) for which the [&hellip;]<\/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-242167","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242167","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=242167"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242167\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=242167"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=242167"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=242167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}