# How do you find all the asymptotes for function #g(x)=e^(x-2)#?

The only asymptote is horizontal, and it is

Since the exponential is defined over the whole real set, you can't have vertical asymptotes. So, let's check the infinite limits:

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To find the asymptotes of the function ( g(x) = e^{x-2} ), you need to consider the behavior of the function as ( x ) approaches positive or negative infinity. Since the exponential function ( e^{x} ) grows without bound as ( x ) increases, there are no horizontal asymptotes for ( g(x) ).

However, there is a vertical asymptote at ( x = 2 ), because when ( x ) approaches 2, the denominator ( e^{x-2} ) approaches 0. Therefore, the vertical asymptote for the function ( g(x) ) is ( x = 2 ).

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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.

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.

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.

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