How to find the asymptotes of #g(x)=5^x#?

1 Answer
May 31, 2016

Answer:

There is a horizontal asymptote of y=0
No vertical asymptote.

Explanation:

As #x# becomes increasingly larger as #x>0# the #5^x# becomes increasingly larger.

So for #x>0" " lim_(x->color(white)()^(+)oo) 5^x=oo#

So as #x# is capable of increasing to #oo# there is no vertical asymptote for #x>0#
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For #x<0# then #5^x = 1/5^x#

As #x# becomes increasing larger (but negative) then #5^x=1/5^x# becomes increasingly smaller.

So for #x<0" " lim_(x->color(white)()^(-)oo) 5^x= 0#

;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
There is a horizontal asymptote of y=0

Tony B