{"id":244524,"date":"2025-07-05T08:07:26","date_gmt":"2025-07-05T08:07:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=244524"},"modified":"2025-07-05T08:07:28","modified_gmt":"2025-07-05T08:07:28","slug":"write-an-equation-for-the-function-graphed-below-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/05\/write-an-equation-for-the-function-graphed-below-3\/","title":{"rendered":"Write an equation for the function graphed below."},"content":{"rendered":"\n

Write an equation for the function graphed below. The y intercept is at (0,-0.2) 5+ 4 3- 2- 1- -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1- -2- -3- -4- -5+ Q y =<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Here is the equation for the function graphed:<\/p>\n\n\n\n

y = -0.8(x – 1) \/ (x\u00b2 – 4)<\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To find the equation of the graphed rational function, we can identify its key features from the image and use them to construct the equation step-by-step.<\/p>\n\n\n\n

    \n
  1. Vertical Asymptotes:<\/strong>\u00a0The graph shows two vertical dashed lines, which are the vertical asymptotes. These occur at x = -2 and x = 2. Vertical asymptotes correspond to the roots of the denominator. Therefore, the denominator of our function will have factors of (x + 2) and (x – 2). Multiplying these gives the denominator: (x + 2)(x – 2) = x\u00b2 – 4.<\/li>\n\n\n\n
  2. Horizontal Asymptote:<\/strong>\u00a0The graph approaches the x-axis (the line y = 0) as x goes to positive and negative infinity. This means the horizontal asymptote is y = 0. For a rational function, this occurs when the degree of the numerator is less than the degree of the denominator. Our denominator has a degree of 2, so this condition is met.<\/li>\n\n\n\n
  3. X-intercept:<\/strong>\u00a0The graph crosses the x-axis at x = 1. The x-intercepts of a rational function correspond to the roots of the numerator. This means the numerator has a factor of (x – 1).<\/li>\n\n\n\n
  4. General Equation:<\/strong>\u00a0Combining these features, we can write a general form for the function:
    y = a * (x – 1) \/ (x\u00b2 – 4)
    Here, ‘a’ is a constant scaling factor that we need to determine.<\/li>\n\n\n\n
  5. Finding the Constant ‘a’:<\/strong>\u00a0The problem states that the y-intercept is at (0, -0.2). We can use this point to solve for ‘a’ by substituting x=0 and y=-0.2 into our general equation:
    -0.2 = a * (0 – 1) \/ (0\u00b2 – 4)
    -0.2 = a * (-1) \/ (-4)
    -0.2 = a \/ 4To isolate ‘a’, we multiply both sides by 4:
    a = 4 * (-0.2)
    a = -0.8<\/li>\n\n\n\n
  6. Final Equation:<\/strong>\u00a0Now we substitute the value of a = -0.8 back into the general equation to get the final answer:
    y = -0.8(x – 1) \/ (x\u00b2 – 4)<\/strong><\/li>\n<\/ol>\n\n\n\n

    This equation can also be written as y = (-0.8x + 0.8) \/ (x\u00b2 – 4)<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Write an equation for the function graphed below. The y intercept is at (0,-0.2) 5+ 4 3- 2- 1- -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1- -2- -3- -4- -5+ Q y = The Correct Answer and Explanation is: Here is the equation for the function graphed: […]<\/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-244524","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244524","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=244524"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244524\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=244524"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=244524"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=244524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}