Question

What are the asymptotes of `y=1/(x-2)` and how do you graph the function?

Answer 1

Vertical asymptote: `x=2` and horizontal asymptote: `y=0`
Graph - Rectangular hyperbola as below.

Explanation:

`y = 1/(x-2)`

`y` is defined for `x in (-oo,2) uu (2,+oo)`

Consider `lim_(x->2^+) y =+oo`

And `lim_(x->2^-) y =-oo`

Hence, `y` has a vertical asymptote `x=2`

Now, consider `lim_(x->oo) y =0`

Hence, `y` has a horizontal asymptote `y=0`

`y` is a rectangular hyperbola with the graph below.

graph{1/(x-2) [-10, 10, -5, 5]}