How do you find the asymptotes for #f(x) = e^(-x) #?

Answer 1

Hence #x->+oo# , #f(x)->0# and #x->-oo# is #f(x)->+oo# and because #e^-x>0# the only asymptote is the horizontal axis yy'

The graph of #f# is

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Answer 2

Theodore Amidon

To find the asymptotes for ( f(x) = e^{-x} ), you need to consider the behavior of the function as ( x ) approaches positive or negative infinity.

As ( x ) approaches positive infinity (( x \to +\infty )), ( e^{-x} ) approaches 0. Therefore, there is a horizontal asymptote at ( y = 0 ) or the x-axis is the asymptote.
As ( x ) approaches negative infinity (( x \to -\infty )), ( e^{-x} ) also approaches 0. Thus, there is another horizontal asymptote at ( y = 0 ).

In summary, the function ( f(x) = e^{-x} ) has horizontal asymptotes at ( y = 0 ), which are the x-axis in both directions.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.