# How do you find the asymptotes for y = (4 x + 6)/(x - 1) ?

Jun 24, 2016

vertical asymptote x = 1
horizontal asymptote y =4

#### Explanation:

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

solve : x - 1 = 0 → x = 1 is the asymptote

Horizontal asymptotes occur as

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

divide terms on numerator/denominator by x

((4x)/x+6/x)/(x/x-1/x)=(4+6/x)/(1-1/x

as $x \to \pm \infty , y \to \frac{4 + 0}{1 - 0}$

$\Rightarrow y = 4 \text{ is the asymptote}$
graph{(4x+6)/(x-1) [-20, 20, -10, 10]}