{"id":247209,"date":"2025-07-07T15:21:29","date_gmt":"2025-07-07T15:21:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=247209"},"modified":"2025-07-07T15:21:32","modified_gmt":"2025-07-07T15:21:32","slug":"the-graph-of-y-log-x-was-transformed-to","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/07\/the-graph-of-y-log-x-was-transformed-to\/","title":{"rendered":"The graph of y = log(-x) was transformed to"},"content":{"rendered":"\n

The graph of y = log(-x) was transformed to y = -3log(2x + 4) – 1. Where did the point (10, 1) move to?<\/p>\n\n\n\n

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

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

The given function undergoes several transformations. Let’s break them down step-by-step to see how the point (10, 1) moves.<\/p>\n\n\n\n

Original Function:<\/h3>\n\n\n\n

The original graph is given by y=log\u2061(x)y = \\log(x)y=log(x), which is a logarithmic function with a vertical asymptote at x=0x = 0x=0 and passes through the point (1, 0).<\/p>\n\n\n\n

Transformed Function:<\/h3>\n\n\n\n

The transformed function is y=\u22123log\u2061(2x+4)\u22121y = -3 \\log(2x + 4) – 1y=\u22123log(2x+4)\u22121. To analyze the transformation, we must consider each operation one by one:<\/p>\n\n\n\n

    \n
  1. Horizontal Shift:<\/strong>
    y=log\u2061(2x+4)y = \\log(2x + 4)y=log(2x+4) is the result of shifting y=log\u2061(x)y = \\log(x)y=log(x) horizontally. To find the horizontal shift, set 2x+4=02x + 4 = 02x+4=0. Solving for xxx, we get: 2x=\u22124\u21d2x=\u22122.2x = -4 \\quad \\Rightarrow \\quad x = -2.2x=\u22124\u21d2x=\u22122. This means the graph of y=log\u2061(2x+4)y = \\log(2x + 4)y=log(2x+4) is shifted 2 units to the left.<\/li>\n\n\n\n
  2. Vertical Stretch and Reflection:<\/strong>
    The term \u22123-3\u22123 outside the logarithmic function causes a vertical stretch by a factor of 3 and a reflection across the x-axis. So, all y-values are multiplied by -3.<\/li>\n\n\n\n
  3. Vertical Shift:<\/strong>
    The term \u22121-1\u22121 at the end of the function shifts the entire graph 1 unit downward.<\/li>\n<\/ol>\n\n\n\n

    Transformation of the Point (10, 1):<\/h3>\n\n\n\n

    To see where the point (10, 1) moves, substitute x=10x = 10x=10 into the transformed function:y=\u22123log\u2061(2(10)+4)\u22121=\u22123log\u2061(20+4)\u22121=\u22123log\u2061(24)\u22121.y = -3 \\log(2(10) + 4) – 1 = -3 \\log(20 + 4) – 1 = -3 \\log(24) – 1.y=\u22123log(2(10)+4)\u22121=\u22123log(20+4)\u22121=\u22123log(24)\u22121.<\/p>\n\n\n\n

    Now, calculate log\u2061(24)\\log(24)log(24). Using the approximation log\u2061(24)\u22481.3802\\log(24) \\approx 1.3802log(24)\u22481.3802:y=\u22123(1.3802)\u22121=\u22124.1406\u22121=\u22125.1406.y = -3(1.3802) – 1 = -4.1406 – 1 = -5.1406.y=\u22123(1.3802)\u22121=\u22124.1406\u22121=\u22125.1406.<\/p>\n\n\n\n

    Thus, the point (10, 1) moves to approximately (10, -5.14).<\/p>\n\n\n\n

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

    After the transformations, the point (10,1)(10, 1)(10,1) moves to (10,\u22125.14)(10, -5.14)(10,\u22125.14).<\/p>\n\n\n\n

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

    The graph of y = log(-x) was transformed to y = -3log(2x + 4) – 1. Where did the point (10, 1) move to? The Correct Answer and Explanation is: The given function undergoes several transformations. Let’s break them down step-by-step to see how the point (10, 1) moves. Original Function: The original graph is […]<\/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-247209","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/247209","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=247209"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/247209\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=247209"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=247209"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=247209"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}