How do you find vertical, horizontal and oblique asymptotes for #g(x)=5^x#?

1 Answer
Sep 5, 2017

Answer:

There will be a horizontal asymptote at #y = 0#.

Explanation:

The domain of any exponential function is #{x| x in RR}#, so no vertical asymptotes.

As for horizontal asymptotes, the following limit will be determinative:

#lim_(x-> -oo) 5^x#

Calling the limit #L#, we have:

#L = lim_(x->-oo) 5^x#

If we think about it, we realize that the closer the number #x = a# gets to #-oo#, the closer #L# will get to #0#. This is because #a^-n = 1/a^n#, and #1/oo = 0#.

So something like #5^-1000# would be very close to #0#. Therefore, we can say that #g(x)# has a horizontal asymptote at #y = 0#.

There will be no oblique asymptote for #g(x)#.

Hopefully this helps!