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

1 Answer
May 16, 2017

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

Explanation:

Given: y = -3/xy=3x

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