{"id":147177,"date":"2024-10-02T14:03:05","date_gmt":"2024-10-02T14:03:05","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=147177"},"modified":"2024-10-02T14:03:07","modified_gmt":"2024-10-02T14:03:07","slug":"how-to-identify-the-parent-function-given-an-equation","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/02\/how-to-identify-the-parent-function-given-an-equation\/","title":{"rendered":"How to identify the parent function given an equation"},"content":{"rendered":"\n

How to identify the parent function given an equation ?<\/p>\n\n\n\n

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

Identifying the parent function from a given equation involves recognizing the basic function type it resembles and understanding how transformations, like shifts, stretches, and reflections, modify that parent function. A parent function is the simplest form of a function in a family of functions, serving as a reference point for more complex variations. Here’s how to identify it:<\/p>\n\n\n\n

Steps to Identify the Parent Function<\/h3>\n\n\n\n
    \n
  1. Determine the Type of Function<\/strong>:
    First, identify if the function is linear, quadratic, cubic, absolute value, exponential, logarithmic, trigonometric, or another type. The form of the equation often indicates the function type.<\/li>\n<\/ol>\n\n\n\n
      \n
    • Linear functions<\/strong> are of the form ( f(x) = mx + b ).<\/li>\n\n\n\n
    • Quadratic functions<\/strong> are in the form ( f(x) = ax^2 + bx + c ).<\/li>\n\n\n\n
    • Cubic functions<\/strong> take the form ( f(x) = ax^3 + bx^2 + cx + d ).<\/li>\n\n\n\n
    • Absolute value functions<\/strong> are expressed as ( f(x) = |x| ).<\/li>\n\n\n\n
    • Exponential functions<\/strong> can be written as ( f(x) = a \\cdot b^x ).<\/li>\n\n\n\n
    • Logarithmic functions<\/strong> are ( f(x) = \\log_b(x) ).<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Look for Transformations<\/strong>:
        If the equation includes transformations (like ( f(x) = a(x-h)^n + k )), analyze these modifications. The terms ( h ) and ( k ) indicate horizontal and vertical shifts, respectively, while ( a ) indicates a stretch or compression.<\/li>\n\n\n\n
      2. Simplify the Equation<\/strong>:
        If possible, simplify the equation to its basic form to reveal the parent function. For example, in the equation ( f(x) = 2(x-3)^2 + 5 ), we can see it’s a quadratic function, with the parent function being ( f(x) = x^2 ).<\/li>\n<\/ol>\n\n\n\n

        Example<\/h3>\n\n\n\n

        Consider the equation ( f(x) = -3(x + 2)^2 + 1 ). Here, we recognize that it is derived from the quadratic parent function ( f(x) = x^2 ). The transformations indicate it is vertically stretched by a factor of 3, reflected over the x-axis, and shifted left by 2 and up by 1.<\/p>\n\n\n\n

        By following these steps, one can effectively identify the parent function from a given equation.<\/p>\n","protected":false},"excerpt":{"rendered":"

        How to identify the parent function given an equation ? The Correct Answer and Explanation is : Identifying the parent function from a given equation involves recognizing the basic function type it resembles and understanding how transformations, like shifts, stretches, and reflections, modify that parent function. A parent function is the simplest form of a […]<\/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-147177","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/147177","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=147177"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/147177\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=147177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=147177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=147177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}