# How do you find all the asymptotes for function #y=1/(2x+4)#?

The function will have a vertical and horizontal asymptotes.

This function has two asymptotes:

Graphically we can see them: graph{1/(2x+4) [-10, 10, -5, 5]}

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To find the asymptotes of the function ( y = \frac{1}{2x + 4} ), you need to identify vertical and horizontal asymptotes.

Vertical Asymptote: Vertical asymptotes occur where the denominator of the rational function becomes zero but the numerator does not. In this case, the denominator ( 2x + 4 ) becomes zero when ( x = -2 ). So, there's a vertical asymptote at ( x = -2 ).

Horizontal Asymptote: To find horizontal asymptotes, consider the behavior of the function as ( x ) approaches positive or negative infinity. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ).

Therefore, the function ( y = \frac{1}{2x + 4} ) has a vertical asymptote at ( x = -2 ) and a horizontal asymptote at ( 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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