# How do you find the vertical, horizontal or slant asymptotes for #(x+3)/(x^2-9)#?

This function has a horizontal asymptote

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To find the vertical asymptotes of the function ( \frac{x + 3}{x^2 - 9} ), we need to identify the values of ( x ) for which the denominator becomes zero, since division by zero is undefined.

The denominator ( x^2 - 9 ) can be factored as ( (x + 3)(x - 3) ). Therefore, the function will have vertical asymptotes at ( x = -3 ) and ( x = 3 ) because these are the values that make the denominator zero.

To find horizontal or slant asymptotes, we need to compare the degrees of the numerator and denominator.

In this case, the degree of the numerator is 1, and the degree of the denominator is 2. Since the degree of the denominator is greater, the function has a horizontal asymptote at ( y = 0 ).

There are no slant asymptotes for this function because the degree of the numerator is not greater than the degree of the denominator by exactly one.

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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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