# What are the asymptote(s) and hole(s), if any, of # f(x) =(x^2-x-2)/(x+2)#?

Vertical asymptote of-2

An horizontal asymptote is created where the top and the bottom of the fraction don't cancel out. Whilst a hole is when you can cancel out.

So lets factorise the top

So as the denominator can't be canceled out by dividing a factor in the top and the bottom it is an asymptote rather than a hole.

graph{((x-2)(x+1))/(x+2) [-51.38, 38.7, -26.08, 18.9]}

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The function f(x) = (x^2-x-2)/(x+2) has a vertical asymptote at x = -2 and a hole at x = 1.

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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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