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

vertical asymptote at x = 2

horizontal asymptote

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.

solve : 2(x - 2 ) = 0 → x = 2 is the equation.

If the degree of the numerator and denominator are equal, as in this case , both of degree 1.Then the equation can be found by taking the ratio of leading coefficients.

Here is the graph of the function to illustrate. graph{(x+1)/(2x-4) [-11.25, 11.25, -5.625, 5.625]}

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To find the asymptotes of the function ( y = \frac{x + 1}{2x - 4} ), we need to examine its behavior as ( x ) approaches certain values.

- Vertical asymptote: Set the denominator equal to zero and solve for ( x ). Any value of ( x ) that makes the denominator zero will result in a vertical asymptote. [ 2x - 4 = 0 ] [ 2x = 4 ] [ x = 2 ]

Therefore, the vertical asymptote is ( x = 2 ).

- 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 degree of the numerator is equal to the degree of the denominator, divide the leading coefficients to find the horizontal asymptote.

The degree of the numerator is 1, and the degree of the denominator is also 1. Therefore, we divide the leading coefficients. [ \frac{1}{2} ]

So, the horizontal asymptote is ( y = \frac{1}{2} ).

Therefore, the asymptotes for ( y = \frac{x + 1}{2x - 4} ) are ( x = 2 ) (vertical asymptote) and ( y = \frac{1}{2} ) (horizontal asymptote).

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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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