{"id":5223,"date":"2025-07-10T10:25:40","date_gmt":"2025-07-10T10:25:40","guid":{"rendered":"https:\/\/skilledprofessors.com\/?p=5223"},"modified":"2025-07-10T10:25:40","modified_gmt":"2025-07-10T10:25:40","slug":"assignment-rational-functions","status":"publish","type":"post","link":"https:\/\/writezilas.com\/essays\/assignment-rational-functions\/","title":{"rendered":"Assignment: Rational Functions"},"content":{"rendered":"\n

<\/p>

\t\t\t\t\t\t\t\t\t\t<\/span>\/10K\u00a0<\/span>

  • State a possible rational function that satisfies the following conditions<\/span>: <\/span>\u00a0\u00a0<\/span>it has these asymptotes\u00a0x=-3x=+2\u00a0y=3<\/span><\/p><\/li>and\u00a0<\/span>

  • it intersects the x axis at 1 and 3<\/span>The presence of the vertical asymptotes x=\u22123 and x=2 implies that the denominator also contains factors (x+3) and (x\u22122).<\/span><\/p><\/li>

  • <\/li>

  • It follows that the horizontal asymptote y=3 indicates that upon simplification, dividing the leading coefficients of both the numerator and denominator must yield 3.<\/span><\/p><\/li>

  • <\/li>

  • From graph, it is clear that the x-intercepts are situated at x=1 and x=3. This implies that the numerator must comprise factors (x\u22121) and (x\u22123).<\/span>Explain by showing all steps how your rational functions satisfies the conditions<\/span> <\/span>above<\/span>. <\/span>\u00a0\u00a0<\/span><\/p><\/li>The vertical asymptotes at x=\u22123 and x=2 can be attributed to the denominator equations which included the factors (x+3) and (x\u22122) respectively. Thus the function is undefined at these values leading to the vertical asymptotes.The horizontal line at y=3 is known because the degrees of both the numerator and denominator are equal; 3 is in the numerator and 1 in the denominator leading to a horizontal asymptote of y=3.Function therefore has x-intercepts at x=1 and x=3 where function becomes zeros as the numerator contains (x\u22121) and (x\u22123) respectively.<\/span><\/p><\/b><\/p>\n","protected":false},"excerpt":{"rendered":"

    \/10K\u00a0 State a possible rational function that satisfies the following conditions: \u00a0\u00a0it has these asymptotes\u00a0x=-3x=+2\u00a0y=3 and\u00a0 it intersects the x axis at 1 and 3The presence of the vertical asymptotes x=\u22123 and x=2 implies that the denominator also contains factors (x+3) and (x\u22122). It follows that the horizontal asymptote y=3 indicates that upon simplification, dividing…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"footnotes":""},"categories":[16],"tags":[],"class_list":["post-5223","post","type-post","status-publish","format-standard","hentry","category-blog"],"_links":{"self":[{"href":"https:\/\/writezilas.com\/essays\/wp-json\/wp\/v2\/posts\/5223","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/writezilas.com\/essays\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/writezilas.com\/essays\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/writezilas.com\/essays\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/writezilas.com\/essays\/wp-json\/wp\/v2\/comments?post=5223"}],"version-history":[{"count":0,"href":"https:\/\/writezilas.com\/essays\/wp-json\/wp\/v2\/posts\/5223\/revisions"}],"wp:attachment":[{"href":"https:\/\/writezilas.com\/essays\/wp-json\/wp\/v2\/media?parent=5223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/writezilas.com\/essays\/wp-json\/wp\/v2\/categories?post=5223"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/writezilas.com\/essays\/wp-json\/wp\/v2\/tags?post=5223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}