{"id":137,"date":"2014-11-20T18:16:33","date_gmt":"2014-11-20T18:16:33","guid":{"rendered":"https:\/\/blue-mathbelt.marjoriesayer.com\/?p=137"},"modified":"2017-07-15T15:48:28","modified_gmt":"2017-07-15T15:48:28","slug":"week-4-rational-functions-day-4","status":"publish","type":"post","link":"https:\/\/blue-mathbelt.marjoriesayer.com\/?p=137","title":{"rendered":"Week 4: Rational Functions &#8211; Day 4"},"content":{"rendered":"<p>Horizontal Asymptotes (end behavior, symmetry)<\/p>\n<p>If the degree of the numerator of a rational function is less than the degree of the denominator, the function has a horizontal asymptote. Use division by the highest power of x to determine the equation of the horizontal asymptote.<\/p>\n<p>If the degree of the numerator is one more than the denominator, there is a slant asymptote. Use long division to find the equation of the slant asymptote.<\/p>\n<p>If the degree of the numerator is two or more than the denominator, the end behavior of the function does not follow a linear asymptote. Instead, it is similar to that of a polynomial of the same degree as the difference between numerator and denominator.<\/p>\n<p>What is the end behavior of each of these functions? If there is a horizontal or slant asymptote, what is its equation?<\/p>\n<p>1. f(x) = (2x + 1) \/ (x &#8211; 4)<\/p>\n<p>2. f(x) = (x<sup>2<\/sup> + 3) \/ (x &#8211; 1)<\/p>\n<p>3. f(x) = (3x<sup>4<\/sup> &#8211; x<sup>3<\/sup> + 5) \/ (x<sup>2<\/sup> + 7)<\/p>\n<p>4. f(x) = 17 \/ (x<sup>2<\/sup> + 4x &#8211; 5)<\/p>\n<p>5. f(x) = (6x<sup>2<\/sup> + 1) \/ (3x<sup>2<\/sup> &#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>Horizontal Asymptotes (end behavior, symmetry) If the degree of the numerator of a rational function is less than the degree of the denominator, the function has a horizontal asymptote. Use division by the highest power of x to determine the equation of the horizontal asymptote. If the degree of the numerator is one more than [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-137","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\/137","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=137"}],"version-history":[{"count":4,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts\/137\/revisions"}],"predecessor-version":[{"id":155,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts\/137\/revisions\/155"}],"wp:attachment":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=137"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=137"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=137"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}