# How do you find all the asymptotes for function #y=1/x#?

Asymptotes are where the function basically has a vertical "no crossing", "restricted" line. Generally, no part of the function should cross an asymptote.

graph{1/x [-10, 10, -5, 5]}

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To find the asymptotes for the function ( y = \frac{1}{x} ), we need to consider both vertical and horizontal asymptotes.

Vertical asymptotes occur where the denominator of the function approaches zero while the numerator remains non-zero. For ( y = \frac{1}{x} ), the vertical asymptote occurs at ( x = 0 ).

Horizontal asymptotes occur as ( x ) approaches positive or negative infinity. For ( y = \frac{1}{x} ), there is a horizontal asymptote at ( y = 0 ).

Therefore, the asymptotes for the function ( y = \frac{1}{x} ) are:

- Vertical asymptote: ( x = 0 )
- Horizontal asymptote: ( y = 0 ).

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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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