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

The asymptotes are $y = 1$ and $x = 6$

#### Explanation:

To find the vertical asymptote, we only need to take note the value approached by x when y is made to increase positively or negatively

as y is made to approach $+ \infty$ , the value of (x-6) approaches zero and that is when x approaches +6.

Therefore, $x = 6$ is a vertical asymptote.

Similarly, To find the horizontal asymptote, we only need to take note the value approached by y when x is made to increase positively or negatively

as x is made to approach $+ \infty$ , the value of y approaches 1.

${\lim}_{x \text{ "approach +-oo) y=lim_(x " } a p p r o a c h \pm \infty} \left(\frac{1}{1 - \frac{6}{x}}\right) = 1$

Therefore, $y = 1$ is a horizontal asymptote.

kindly see the graph of

$y = \frac{x}{x - 6}$.
graph{y=x/(x-6)[-20,20,-10,10]}

and the graph of the asymptotes $x = 6$ and $y = 1$ below.
graph{(y-10000000x+6*10000000)(y-1)=0[-20,20,-10,10]}
have a nice day!