# What are the horizontal and vertical asymptotes on the graph of #f(x) = (x -1)/(x^2 + 2x + 1)#?

•Vertical asymptote at

#x = -1#

•Horizontal asymptote at#y = 0# .

We have a couple of limits to evaluate.

First limit

Second Limit

Therefore, our asymptotes will be:

We now verify graphically.

graph{(x - 1)/(x + 1)^2 [-10, 10, -5, 5]}

Hopefully this helps!

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The horizontal asymptote is y = 0 and there is no vertical asymptote.

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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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