The horizontal asymptote of ##y=e^x## is ##y=0##.<\/p>\n
The graph of ##y=e^x## is asymptotic to the negative x-axis only. Horizontal asymptotes of a graph are related to the end behavior of a function. Since<\/p>\n
##lim_(x->-oo)e^x=0##<\/p>\n
the horizontal asymptote is ##y=0##.<\/p>\n
This is because, for negative values of x,<\/p>\n
##e^x=1\/(e^|x|##<\/p>\n
And, as ##x->-oo##, ##1\/e^|x|## will approach zero.<\/p>\n
See image below for a graphical interpretation.<\/p>\n
Notice that,<\/p>\n
##lim_(x->oo)e^x=oo##<\/p>\n
So, as increases without bound, so does y.<\/p>\n","protected":false},"excerpt":{"rendered":"
The horizontal asymptote of ##y=e^x## is ##y=0##. The graph of ##y=e^x## is asymptotic to the negative x-axis only. Horizontal asymptotes of a graph are related to the end behavior of a function. Since ##lim_(x->-oo)e^x=0## the horizontal asymptote is ##y=0##. This Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-67733","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/67733","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=67733"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/67733\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=67733"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=67733"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=67733"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}