Question

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

Answer 1

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]}