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

Jul 6, 2017

$\text{vertical asymptote at } x = 2$
$\text{horizontal asymptote at } y = \frac{1}{2}$

#### Explanation:

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.

$\text{solve " 2x-4=0rArrx=2" is the asymptote}$

$\text{horizontal asymptotes occur as }$

${\lim}_{x \to \pm \infty} , y \to c \text{ (a constant)}$

$\text{divide terms on numerator/denominator by x}$

$y = \frac{\frac{x}{x} + \frac{1}{x}}{\frac{2 x}{x} - \frac{4}{x}} = \frac{1 + \frac{1}{x}}{2 - \frac{4}{x}}$

as $x \to \pm \infty , y \to \frac{1 + 0}{2 - 0}$

$\Rightarrow y = \frac{1}{2} \text{ is the asymptote}$
graph{(x+1)/(2x-4) [-10, 10, -5, 5]}