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

1 Answer

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 +oo , 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 +oo , the value of y approaches 1.

lim_(x " "approach +-oo) y=lim_(x " "approach +-oo)(1/(1-6/x))=1

Therefore, y=1 is a horizontal asymptote.

kindly see the graph of

y=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!