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

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Answer 1 · 2017-05-16T04:02:40

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

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#