Question

How do you graph `f(x)=-3/x` using holes, vertical and horizontal asymptotes, x and y intercepts?

Answer 1

See graph

no holes.

Explanation:

Set `x=0` to solve for `y` intercept:

`f(x)=-3/x`

`-3/0` in undefined so no `y` intercept exists

Set `f(x)=y=0` to solve for `x` intercept(s):

`0=-3/x`

`0=-3` is not possible so no `x` intercept(s) exist.

There are no holes because you cannot cancel any factors with `x` in them from the denominator.

Set the denominator=0 to solve fo asymptotes:

`x=0` so there is a vertical asymptote at `y=0`.

`x -> +-oo, f(x) -> 0` so there is a horizontal asymptote at `x=0`

graph{-3/x [-10, 10, -5, 5]}