{"id":189678,"date":"2025-02-10T07:12:50","date_gmt":"2025-02-10T07:12:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=189678"},"modified":"2025-02-10T07:12:52","modified_gmt":"2025-02-10T07:12:52","slug":"determine-algebraically-whether-the-given-function-is-even-odd-or-neither","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/10\/determine-algebraically-whether-the-given-function-is-even-odd-or-neither\/","title":{"rendered":"Determine algebraically whether the given function is even, odd, or neither"},"content":{"rendered":"\n

Determine algebraically whether the given function is even, odd, or neither. -9x h(x) = 4x-2<\/p>\n\n\n\n

A Odd <\/p>\n\n\n\n

B Even <\/p>\n\n\n\n

C Neither<\/p>\n\n\n\n

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

To determine whether the function ( h(x) = 4x – 2 ) is even, odd, or neither, we need to evaluate the function using the definitions of even and odd functions.<\/p>\n\n\n\n

Definitions:<\/h3>\n\n\n\n
    \n
  1. Even Function<\/strong>: A function ( f(x) ) is even if for all ( x ) in the domain of the function, ( f(-x) = f(x) ).<\/li>\n\n\n\n
  2. Odd Function<\/strong>: A function ( f(x) ) is odd if for all ( x ) in the domain of the function, ( f(-x) = -f(x) ).<\/li>\n<\/ol>\n\n\n\n

    Step 1: Check if the function is even.<\/h3>\n\n\n\n

    For the function ( h(x) = 4x – 2 ), we need to evaluate ( h(-x) ):<\/p>\n\n\n\n

    [
    h(-x) = 4(-x) – 2 = -4x – 2
    ]<\/p>\n\n\n\n

    Now, we compare ( h(-x) ) to ( h(x) ):<\/p>\n\n\n\n

    [
    h(x) = 4x – 2
    ]<\/p>\n\n\n\n

    Clearly, ( h(-x) \\neq h(x) ), because ( -4x – 2 \\neq 4x – 2 ). This means the function is not even<\/strong>.<\/p>\n\n\n\n

    Step 2: Check if the function is odd.<\/h3>\n\n\n\n

    Next, we check if ( h(-x) = -h(x) ). We already know from the previous step that:<\/p>\n\n\n\n

    [
    h(-x) = -4x – 2
    ]
    and
    [
    -h(x) = -(4x – 2) = -4x + 2
    ]<\/p>\n\n\n\n

    Since ( h(-x) = -4x – 2 ) and ( -h(x) = -4x + 2 ), we see that ( h(-x) \\neq -h(x) ). Therefore, the function is not odd<\/strong>.<\/p>\n\n\n\n

    Conclusion:<\/h3>\n\n\n\n

    Since the function is neither even nor odd, the correct answer is C) Neither<\/strong>.<\/p>\n\n\n\n

    300-word Explanation:<\/h3>\n\n\n\n

    To determine whether a function is even, odd, or neither, we use algebraic tests based on how the function behaves when we replace ( x ) with ( -x ).<\/p>\n\n\n\n

      \n
    1. Even Functions<\/strong>: An even function satisfies the condition that ( f(-x) = f(x) ) for all values of ( x ) in the function’s domain. In other words, the function\u2019s graph is symmetric about the y-axis.<\/li>\n\n\n\n
    2. Odd Functions<\/strong>: An odd function satisfies the condition that ( f(-x) = -f(x) ) for all ( x ) in the function’s domain. The graph of an odd function is symmetric with respect to the origin.<\/li>\n<\/ol>\n\n\n\n

      In our case, the given function is ( h(x) = 4x – 2 ). When we calculate ( h(-x) ), we get ( -4x – 2 ), which is not equal to ( h(x) = 4x – 2 ). Hence, the function is not even.<\/p>\n\n\n\n

      Furthermore, when we calculate ( -h(x) ), we find that ( -h(x) = -4x + 2 ), which is also not equal to ( h(-x) = -4x – 2 ). Hence, the function is not odd.<\/p>\n\n\n\n

      Since the function fails to satisfy the conditions for both even and odd functions, the correct classification for ( h(x) = 4x – 2 ) is that it is neither even nor odd. Thus, the correct answer is C) Neither<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Determine algebraically whether the given function is even, odd, or neither. -9x h(x) = 4x-2 A Odd B Even C Neither The Correct Answer and Explanation is : To determine whether the function ( h(x) = 4x – 2 ) is even, odd, or neither, we need to evaluate the function using the definitions of […]<\/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-189678","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189678","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=189678"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189678\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=189678"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=189678"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=189678"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}