Question

What are the asymptotes of `y=-3/x` and how do you graph the function?

Answer 1

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

Explanation:

Given: `y = -3/x`

For Rational functions of the form `(N(x))/(D(x)) = (a_nx^n + ...)/(b_mx^m + ...)`.

To find vertical asymptotes, set `D(x) = 0`:
`D(x) = x = 0`

To find horizontal asymptotes:
When `n < m" "` horizontal asymptote: `" " y = 0`

When `n = m " "` horizontal asymptote: `" " y = a_n/b_m`

When `n > m" "` there is no horizontal asymptote.

For `y = -3/x, " "n = 0, m = 1 " " n< m`

Horizontal asymptote at `y = 0`