# How do you find the Vertical, Horizontal, and Oblique Asymptote given #f(x) =( 2x-3)/(x^2+2)#?

horizontal asymptote at y = 0

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for there values then they are vertical asymptotes.

x has no real solutions hence there are no vertical asymptotes.

Horizontal asymptotes occur as

Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (numerator-degree 1, denominator-degree 2) Hence there are no oblique asymptotes. graph{(2x-3)/(x^2+2) [-10, 10, -5, 5]}

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Vertical asymptote: x = 0 Horizontal asymptote: y = 0 Oblique asymptote: None

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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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