{"id":168481,"date":"2024-11-17T15:18:34","date_gmt":"2024-11-17T15:18:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168481"},"modified":"2024-11-17T15:18:36","modified_gmt":"2024-11-17T15:18:36","slug":"what-are-the-domain-and-range-of-the-function","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/17\/what-are-the-domain-and-range-of-the-function\/","title":{"rendered":"What are the domain and range of the function"},"content":{"rendered":"\n

What are the domain and range of the function?<\/p>\n\n\n\n

f(x)=35×5<\/p>\n\n\n\n

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

To determine the domain and range of the function ( f(x) = 35x^5 ), we must understand the structure of the function and its behavior.<\/p>\n\n\n\n

Domain:<\/h3>\n\n\n\n

The domain<\/strong> of a function consists of all the possible input values (x-values) that will result in a valid output for the function. The function ( f(x) = 35x^5 ) is a polynomial, where ( 35x^5 ) is a product of a constant (35) and a power of ( x ) (specifically, ( x^5 )).<\/p>\n\n\n\n

Polynomials like ( 35x^5 ) are defined for all real numbers, meaning there are no restrictions or undefined values (like division by zero or square roots of negative numbers). Therefore, the domain of ( f(x) = 35x^5 ) is all real numbers.<\/p>\n\n\n\n

Thus, the domain is:
[
\\text{Domain} = (-\\infty, \\infty)
]<\/p>\n\n\n\n

Range:<\/h3>\n\n\n\n

The range<\/strong> of a function consists of all the possible output values (f(x)-values) that the function can produce.<\/p>\n\n\n\n

For ( f(x) = 35x^5 ), the function is a polynomial function of odd degree<\/strong> (degree 5). Let’s analyze how the output behaves as ( x ) changes:<\/p>\n\n\n\n

    \n
  • When ( x ) is positive, ( x^5 ) is also positive, so ( f(x) ) will be positive.<\/li>\n\n\n\n
  • When ( x ) is negative, ( x^5 ) is negative (since raising a negative number to an odd power results in a negative number), so ( f(x) ) will be negative.<\/li>\n\n\n\n
  • As ( x ) approaches infinity (( x \\to \\infty )), ( f(x) ) also goes to infinity (( f(x) \\to \\infty )).<\/li>\n\n\n\n
  • As ( x ) approaches negative infinity (( x \\to -\\infty )), ( f(x) ) goes to negative infinity (( f(x) \\to -\\infty )).<\/li>\n<\/ul>\n\n\n\n

    Therefore, the function ( f(x) = 35x^5 ) can take any real value, meaning its range is also all real numbers.<\/p>\n\n\n\n

    Thus, the range is:
    [
    \\text{Range} = (-\\infty, \\infty)
    ]<\/p>\n\n\n\n

    Conclusion:<\/h3>\n\n\n\n
      \n
    • The domain<\/strong> of ( f(x) = 35x^5 ) is ( (-\\infty, \\infty) ).<\/li>\n\n\n\n
    • The range<\/strong> of ( f(x) = 35x^5 ) is ( (-\\infty, \\infty) ).<\/li>\n<\/ul>\n\n\n\n

      This is because polynomial functions, particularly those with odd degrees, have domains and ranges that cover all real numbers.<\/p>\n","protected":false},"excerpt":{"rendered":"

      What are the domain and range of the function? f(x)=35×5 The Correct Answer and Explanation is: To determine the domain and range of the function ( f(x) = 35x^5 ), we must understand the structure of the function and its behavior. Domain: The domain of a function consists of all the possible input values (x-values) […]<\/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-168481","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168481","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=168481"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168481\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168481"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168481"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168481"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}