Question

How do you find the Vertical, Horizontal, and Oblique Asymptote given `y = (x + 1)/(x - 1)`?

Answer 1

The vertical asymptote is `x=1`
The horizontal asymptote is `y=1`
No oblique asymptote

Explanation:

As you cannot divide by `0`, `x!=1`

The vertical asymptote is `x=1`

As the degree of the numerator `=` the degree of the denominator, there is no oblique asymptote

`lim_(x->+oo)y=lim_(x->+oo)x/x=1`

The horizontal asymptote is `y=1`

graph{(y-(x+1)/(x-1))(y-1)(y-100x+100)=0 [-8.1, 9.674, -4.8, 4.085]}