{"id":4252,"date":"2022-06-10T19:00:40","date_gmt":"2022-06-10T19:00:40","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4252"},"modified":"2022-06-10T19:00:40","modified_gmt":"2022-06-10T19:00:40","slug":"vertical-asymptote-of-a-rational-function","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/10\/vertical-asymptote-of-a-rational-function\/","title":{"rendered":"Vertical Asymptote of a Rational Function"},"content":{"rendered":"\n<p>A\u00a0vertical asymptote\u00a0(VA) of a function is an imaginary vertical line to which its graph appears to be very close but never touch. It is of the form x = some number. Here, &#8220;some number&#8221; is closely connected to the excluded values from the domain. But note that there cannot be a vertical asymptote at x = some number if there is a hole at the same number. A rational function may have one or more vertical asymptotes. So to find the vertical asymptotes of a rational function:<\/p>\n\n\n\n<ul><li>Simplify the function first to cancel all common factors (if any).<\/li><li>Set the denominator = 0 and solve for (x) (or equivalently just get the excluded values from the domain by avoiding the holes).<\/li><\/ul>\n\n\n\n<p><strong>Example:<\/strong>&nbsp;Find the vertical asymptotes of the function f(x) = (x<sup>2<\/sup>&nbsp;+ 5x + 6) \/ (x<sup>2<\/sup>&nbsp;+ x &#8211; 2).<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>We have already seen that this function simplifies to f(x) = (x + 3) \/ (x &#8211; 1).<\/p>\n\n\n\n<p>Setting the denominator to 0, we get<\/p>\n\n\n\n<p>x &#8211; 1 = 0<br>x = 1<\/p>\n\n\n\n<p>Thus, there is a VA of the given rational function is, x = 1.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A\u00a0vertical asymptote\u00a0(VA) of a function is an imaginary vertical line to which its graph appears to be very close but never touch. It is of the form x = some number. Here, &#8220;some number&#8221; is closely connected to the excluded values from the domain. But note that there cannot be a vertical asymptote at x [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[715],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4252"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=4252"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4252\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4252"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4252"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}