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

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

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To find the asymptotes for ( y = \frac{x + 1}{2x - 4} ), you need to determine both the horizontal and vertical asymptotes.

Vertical asymptotes occur where the denominator equals zero, but the numerator doesn't. So, set ( 2x - 4 = 0 ) and solve for ( x ).

( 2x - 4 = 0 ) ( 2x = 4 ) ( x = 2 )

Therefore, there's a vertical asymptote at ( x = 2 ).

To find the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ). If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the numerator is greater, there is no horizontal asymptote.

In this case, the degree of the numerator is 1 and the degree of the denominator is also 1. So, the horizontal asymptote is the ratio of the leading coefficients, which is ( \frac{1}{2} ).

Therefore, the vertical asymptote is ( x = 2 ) and the horizontal asymptote is ( y = \frac{1}{2} ).

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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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