{"id":244226,"date":"2025-07-04T21:48:26","date_gmt":"2025-07-04T21:48:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=244226"},"modified":"2025-07-04T21:48:28","modified_gmt":"2025-07-04T21:48:28","slug":"based-on-the-graph-above-estimate-to-one-decimal-place-the-average-rate-of-change-from-to","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/based-on-the-graph-above-estimate-to-one-decimal-place-the-average-rate-of-change-from-to\/","title":{"rendered":"Based on the graph above, estimate to one decimal place the average rate of change from to"},"content":{"rendered":"\n

Question 19 8 7 6 5 4 3 2 1 -1 1 2 3 4 5 Based on the graph above, estimate to one decimal place the average rate of change from
to<\/p>\n\n\n\n

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

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

Answer:<\/strong> -1.0<\/p>\n\n\n\n

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

The average rate of change of a function over a specific interval represents the slope of the secant line connecting the two endpoints of that interval on the graph. The formula to calculate the average rate of change of a function, let’s call it f(x), from x = a to x = b is:<\/p>\n\n\n\n

Average Rate of Change = (f(b) – f(a)) \/ (b – a)<\/strong><\/p>\n\n\n\n

In this problem, we are asked to find the average rate of change from x = 1<\/strong> to x = 3<\/strong>. Therefore, a = 1 and b = 3.<\/p>\n\n\n\n

Step 1: Find the function values (y-values) from the graph.<\/strong><\/p>\n\n\n\n

First, we need to determine the y-values of the function at x = 1 and x = 3 by reading the provided graph.<\/p>\n\n\n\n

    \n
  • Find f(1):<\/strong>\u00a0Locate x = 1 on the horizontal axis (the x-axis). Move vertically up from this point until you intersect the curve. From this intersection point, move horizontally to the left to read the value on the vertical axis (the y-axis). The graph clearly passes through the point\u00a0(1, 5)<\/strong>. Therefore,\u00a0f(1) = 5<\/strong>.<\/li>\n\n\n\n
  • Find f(3):<\/strong>\u00a0Similarly, locate x = 3 on the horizontal axis. Move vertically up to the curve. From that point on the curve, move horizontally to the left to read the corresponding y-value. The graph passes through the point\u00a0(3, 3)<\/strong>. Therefore,\u00a0f(3) = 3<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    Step 2: Apply the average rate of change formula.<\/strong><\/p>\n\n\n\n

    Now, we substitute the values we found into the formula:<\/p>\n\n\n\n

      \n
    • a = 1, f(a) = f(1) = 5<\/li>\n\n\n\n
    • b = 3, f(b) = f(3) = 3<\/li>\n<\/ul>\n\n\n\n

      Average Rate of Change = (f(3) – f(1)) \/ (3 – 1)
      Average Rate of Change = (3 – 5) \/ (3 – 1)
      Average Rate of Change = -2 \/ 2
      Average Rate of Change = -1<\/p>\n\n\n\n

      Step 3: Format the answer.<\/strong><\/p>\n\n\n\n

      The question asks for the answer to be estimated to one decimal place. To express -1 with one decimal place, we write it as -1.0<\/strong>.<\/p>\n\n\n\n

      This result means that, on average, between x = 1 and x = 3, the function’s value decreases by 1 unit for every 1 unit increase in x<\/p>\n\n\n\n

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

      Question 19 8 7 6 5 4 3 2 1 -1 1 2 3 4 5 Based on the graph above, estimate to one decimal place the average rate of change fromto The Correct Answer and Explanation is: Answer: -1.0 Explanation: The average rate of change of a function over a specific interval represents the slope […]<\/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-244226","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244226","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=244226"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244226\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=244226"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=244226"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=244226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}