Question

How do you graph `f(x)=x/(x-2)` using holes, vertical and horizontal asymptotes, x and y intercepts?

Answer 1

Below

Explanation:

`f(x)=x/(x-2)`
`f(x)=((x-2)+2)/(x-2)`
`f(x)=1+2/(x-2)`

As `x -> oo`, `y ->1`
ie As x approaches a very big number, `2/(x-2)` will become 0
For the vertical asymptote, `x-2 !=0` since the denominator cannot equal to 0.

Therefore, there is a horizontal asymptote at `y=1` and a vertical asymptote at `x=2`

For intercepts,
When `y=0`, `x=0`
When `x=0`, `y=0`

Then, after plotting your intercepts and your asymptotes, you can hopefully see the outline of your graph. Your end points should be approaching the asymptotes but never touching your asymptotes.
graph{x/(x-2) [-10, 10, -5, 5]}