{"id":494,"date":"2022-01-14T12:00:57","date_gmt":"2022-01-14T18:00:57","guid":{"rendered":"https:\/\/blogs.acu.edu\/mu_sigma\/?p=494"},"modified":"2022-01-21T11:24:15","modified_gmt":"2022-01-21T17:24:15","slug":"problem-9-alternative-math-1-14-2022","status":"publish","type":"post","link":"https:\/\/blogs.acu.edu\/mu_sigma\/2022\/01\/14\/problem-9-alternative-math-1-14-2022\/","title":{"rendered":"Problem 9 &#8211; Alternative Math &#8211; 1\/14\/2022"},"content":{"rendered":"<h4>Problem 9 &#8211; Alternative Math<\/h4>\n<p>In an alternative math world suppose that a+b means the maximum of a and b, while a*b means the sum of a and b.\u00a0 For example, 2 + 3 = 3 and 5^2 = 10.\u00a0 In this world, which of the graphs below represents f(x) = x^2 + 2x + 1?\u00a0 \u00a0If you choose (E) please provide a sketch of the correct graph.<\/p>\n<p><a href=\"http:\/\/blogs.acu.edu\/mu_sigma\/files\/2022\/01\/Screen-Shot-2022-01-13-at-11.13.31-AM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-495 \" src=\"http:\/\/blogs.acu.edu\/mu_sigma\/files\/2022\/01\/Screen-Shot-2022-01-13-at-11.13.31-AM-e1642094347361-490x330.png\" alt=\"\" width=\"598\" height=\"365\" \/><\/a>All problem of the week submissions are due by 5:00 PM, Thursday the following week.\u00a0 Please send submissions to mathpotw@acu.edu.<\/p>\n<p>There was only one correct submission from Wyatt Witemeyer.<\/p>\n<h3><strong>Solution<\/strong>:<\/h3>\n<p>The answer is C.\u00a0 Observe that max((x + x), (2+x), 1) is what we have to find to plot the solution.\u00a0 When -infinity &lt; x &lt; -1, then max = 1.\u00a0 When -1 &lt; x &lt; 2, then max = 2 + x.\u00a0 When 2 &lt; x &lt; infinity, then max = x+x&gt;. This means we plot the piecewise function f(x) = { 1, [-infinity, -1],\u00a0 x+2, [-1,2], 2x, [2,infinity]} which is answer choice (C).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problem 9 &#8211; Alternative Math In an alternative math world suppose that a+b means the maximum of a and b, while a*b means the sum of a and b.\u00a0 For example, 2 + 3 = 3 and 5^2 = 10.\u00a0 In this world, which of the graphs below represents f(x) = x^2 + 2x + [&hellip;]<\/p>\n","protected":false},"author":130,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[181534],"tags":[],"class_list":["post-494","post","type-post","status-publish","format-standard","hentry","category-problem-of-the-week"],"_links":{"self":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts\/494","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/users\/130"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/comments?post=494"}],"version-history":[{"count":3,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts\/494\/revisions"}],"predecessor-version":[{"id":499,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts\/494\/revisions\/499"}],"wp:attachment":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/media?parent=494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/categories?post=494"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/tags?post=494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}