Question

How do you find the asymptotes for `y = 2/(x-6)`?

Answer 1

This function has a vertical asymptote at `x=6` and a horizontal asymptote at `y=0`

Explanation:

Vertical asymptotes occur at points which lead to division by zero in the denominator, so in this case, at `x=6`.

Horizontal asymptotes occur at `lim_(x->+-oo)y(x)`, so in this case, at `y=0`.

This is clear from the graph of the function :

graph{2/(x-6) [-5.03, 20.28, -7.45, 5.21]}

Answer 2

vertical asymptote x=6 , horizontal asymptote y=0

Explanation:

To find a vertical asymptote , requires the denominator of a
rational function to be zero.

solve x-6 = 0 hence x = 6 is vertical asymptote

[ A horizontal asymptote can be found when the degree of

the numerator is less than the degree of the denominator ]

here, degree of numerator is 0 , degree of denominator is 1

In this situation the equation is always y = 0

here is the graph of the function to illustrate these.
graph{2/(x-6) [-10, 10, -5, 5]}