Question

How do you find the asymptotes for `y = 6/x`?

Answer 1

Vertical asymptote at `x=0`
Horizontal asymptote at `y=0`

Explanation:

Given
`color(white)("XXX")y=6/x`
This relation ship is defined for all values of `x` except `x=0`;
`x` may approach `0` as closely as we like, but it can never be `=0`;
therefore `x=0` is an asymptote.

As `xrarroo`
`color(white)("XXX")yrarr0`
but `y` is never `=0`;
therefore `y=0` is an asymptote.
graph{y=6/x [-28.86, 28.85, -14.43, 14.43]}