What are the asymptotes for #1/x#?
Have a look:
You can see these two asymptote graphically as the two lines near which the curve (representing your function) tends to get near to: graph{1/x [10, 10, 5, 5]}
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The function ( \frac{1}{x} ) has two types of asymptotes: vertical asymptotes and horizontal asymptotes.

Vertical Asymptotes: Vertical asymptotes occur where the function approaches positive or negative infinity as ( x ) approaches a certain value. For ( \frac{1}{x} ), vertical asymptotes occur where the denominator ( x ) equals zero. Therefore, the vertical asymptote for ( \frac{1}{x} ) is the line ( x = 0 ).

Horizontal Asymptotes: Horizontal asymptotes occur when the function approaches a constant value as ( x ) approaches positive or negative infinity. For ( \frac{1}{x} ), as ( x ) approaches positive or negative infinity, the function approaches zero. Therefore, the horizontal asymptote for ( \frac{1}{x} ) is the line ( y = 0 ) or the xaxis.
In summary:
 Vertical asymptote: ( x = 0 )
 Horizontal asymptote: ( y = 0 ) or the xaxis.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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