How do you find the asymptote of an exponential function?

Answer 1

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

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]}

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Answer 2

Christian Antunez

To find the asymptote of an exponential function, determine the behavior of the function as \( x \) approaches positive or negative infinity. If the exponential function is in the form \( f(x) = a \cdot b^x \), where \( a \) and \( b \) are constants, the horizontal asymptote is at \( y = 0 \) if \( 0 < b < 1 \). If \( b > 1 \), there is no horizontal asymptote.

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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.