How to find the asymptotes of #h(x)=5^(x-2)#?

1 Answer
Feb 22, 2018

Answer:

Take the limits of #h(x)# as #x->+-∞# to determine the horizontal asymptotes.

Explanation:

Take the limits of #h(x)# as #x->+-∞# to determine the function's horizontal asymptotes. We have no vertical asymptotes, as there are no values of #x# that will make this function undefined.

#Lim_(x->∞)5^(x-2)=5^∞=∞# (No asymptotes as we approach #+∞#.

#Lim_(x->-∞)5^(x-2)=5^-∞=1/5^∞=0#

So, #y=0# is this function's only horizontal asymptote, as we approach #y=0# for smaller and smaller values of #x# but never cross/touch it.