Question

How do you find the Horizontal Asymptote of y= (x+2)/(x-6)?

Answer 1

Let's look at this from a common sense point of view.

A horizontal asymptote is usually found by letting the value of x become either very large in the positive direction or very large in the negative direction

suppose we let x = + 1000
the y = 1002/994 which is slightly above 1
as x gets larger and larger the value of y approaches closer and closer to 1, (but still a bit > 1) , the numerator and denominator always differ by 6)
now look at the other end, when x becomes hugely negative,
suppose we let x = - 1000
then y = 1=- 998/-1006 which is slightly below 1

so the horizontal asymptote is y = 1

(approaching 1 from above on the right, and below on the left)