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How do you find the asymptote of an exponential function?

1 Answer
Feb 19, 2016

Answer:

There is no vertical asymptote, as #x# may have any value.

Explanation:

For the horizontal asymptote we look at what happens if we let #x# grow, both positively and negatively.

#x->+oo#
The function will be greater without limit. No asymptote there.

#x->-oo#
The function will get smaller and smaller, not ever quite reaching #0#, so #y=0# is an asymptote, or in 'the language':

#lim_(x->-oo) f(x)=0#
graph{0.1*e^x [-30.37, 20.96, -12.52, 13.15]}