What are the asymptotes for #ln(x-2)#?

1 Answer
Oct 10, 2015

Answer:

Use the fact that it is a translation of #lnx#

Explanation:

The graph of #y=ln(x-2)# is the graph of #y=lnx# translated #2# to the right.

#y=lnx# has vertical asymptote #x=0# (the #y#-axis).

When we translate the graph, we also translate any asymptotes,

so the new graph has asymptote #x=2#.

Note We can also think of the fact that we'll get an asymptote when we try to find #ln0#, which happens for the new graph at #x=2#.

Thirdly
For translations of #lnx#, the asymptote occors at the bounded end of the domain.
The domain of #ln(x-2)# is #(2,oo)# so the asymptote is at #2#.
The asymptote is the vertical line #x=2#.