How do you find all the asymptotes for function #y=1/x#?

1 Answer
Jun 11, 2015

Asymptotes are where the function basically has a vertical "no crossing", "restricted" line. Generally, no part of the function should cross an asymptote.

You cannot divide by #0#, so #1/0# describes a vertical asymptote at #x = 0#. Also, #0 ne 1/x# because #x*0 = 0 ne 1#, so there is a horizontal asymptote at #y = 0#.

graph{1/x [-10, 10, -5, 5]}