{"id":135,"date":"2014-11-18T22:12:54","date_gmt":"2014-11-18T22:12:54","guid":{"rendered":"https:\/\/blue-mathbelt.marjoriesayer.com\/?p=135"},"modified":"2014-11-19T23:04:59","modified_gmt":"2014-11-19T23:04:59","slug":"week-4-rational-functions-day-3","status":"publish","type":"post","link":"https:\/\/blue-mathbelt.marjoriesayer.com\/?p=135","title":{"rendered":"Week 4: Rational Functions &#8211; Day 3"},"content":{"rendered":"<p>Vertical Asymptotes<\/p>\n<p>Asymptotes are lines that the graph of a function approaches. A vertical line in the x-y plane is a line that goes to plus and minus infinity. So vertical asymptotes indicate that the values of a function approach infinity (or minus infinity) as x approaches a finite value.<\/p>\n<p>Example notes: The function f(x) = 1\/(x &#8211; 1) has a vertical asymptote at x = 1. But the function g(x) = (x<sup>2<\/sup> &#8211; 1)\/(x &#8211; 1) does not have a vertical asymptote at x = 1. As long as x is not equal to 1, the function g(x) is equivalent to x + 1, which has no vertical asymptote. (Factor and simplify g(x) to make sure that this is true.)<\/p>\n<p>Which functions below have vertical asymptotes? If there are any vertical asymptotes, what are their equations?<\/p>\n<p>1. f(x) = 3 \/ (x &#8211; 2)<\/p>\n<p>2. f(x) = (x<sup>3<\/sup> + x)\/x<\/p>\n<p>3. f(x) = x \/ (x<sup>2<\/sup> + 5)<\/p>\n<p>4. f(x) = (2x<sup>3<\/sup> &#8211; 32) \/ (x<sup>2<\/sup> &#8211; 6x + 5)<\/p>\n<p>5. f(x) = 1 &#8211; 1\/x + 2\/(x &#8211; 1)<\/p>\n<p><a title=\"Week 4: Rational Functions \u2013 Answers\" href=\"https:\/\/blue-mathbelt.marjoriesayer.com\/?page_id=129\">Answers<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Vertical Asymptotes Asymptotes are lines that the graph of a function approaches. A vertical line in the x-y plane is a line that goes to plus and minus infinity. So vertical asymptotes indicate that the values of a function approach infinity (or minus infinity) as x approaches a finite value. Example notes: The function f(x) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-135","post","type-post","status-publish","format-standard","hentry","category-rational-functions"],"_links":{"self":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts\/135","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=135"}],"version-history":[{"count":5,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts\/135\/revisions"}],"predecessor-version":[{"id":152,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts\/135\/revisions\/152"}],"wp:attachment":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}