{"id":4248,"date":"2022-06-10T18:59:28","date_gmt":"2022-06-10T18:59:28","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4248"},"modified":"2022-06-10T18:59:28","modified_gmt":"2022-06-10T18:59:28","slug":"range-of-rational-function","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/10\/range-of-rational-function\/","title":{"rendered":"Range of Rational Function"},"content":{"rendered":"\n<p>The range of a rational function is the set of all outputs (y-values) that it produces. To find the range of a rational function y= f(x):<\/p>\n\n\n\n<ul><li>If we have f(x) in the equation, replace it with y.<\/li><li>Solve the equation for x.<\/li><li>Set the denominator of the resultant equation \u2260 0 and solve it for y.<\/li><li>Set of all real numbers other than the values of y mentioned in the last step is the range.<\/li><\/ul>\n\n\n\n<p><strong>Example:<\/strong>&nbsp;Find the range of f(x) = (2x + 1) \/ (3x &#8211; 2).<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us replace f(x) with y. Then y = (2x + 1) \/ (3x &#8211; 2). Now, we will solve this for x.<\/p>\n\n\n\n<p>(3x &#8211; 2) y = (2x + 1)<br>3xy &#8211; 2y = 2x + 1<br>3xy &#8211; 2x = 2y + 1<br>x (3y &#8211; 2) = (2y + 1)<br>x = (2y + 1) \/ (3y &#8211; 2)<\/p>\n\n\n\n<p>Now (3y &#8211; 2) \u2260 0<br>y \u2260 2\/3<\/p>\n\n\n\n<p>So the range = {y \u2208 R | y \u2260 2\/3}<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The range of a rational function is the set of all outputs (y-values) that it produces. To find the range of a rational function y= f(x): If we have f(x) in the equation, replace it with y. Solve the equation for x. Set the denominator of the resultant equation \u2260 0 and solve it for [&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\/4248"}],"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=4248"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4248\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4248"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4248"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4248"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}