Question

What is the vertical asymptote of 1/x?

Answer 1

The vertical asymptote of `1/x` occurs at `x=0`.

Vertical asymptotes occur at `x`-values for which the limit of the function as we approach these values from the right or the left (or both) approaches `+-oo`. Thus, in the example above, we look for when the function `f(x) = 1/x` approaches `+-oo`.

In this case, this will only occur when the denominator is 0. Since our denominator is simply `x`, this means our only vertical asymptote occurs at `x=0`.

For a more in-depth examination of vertical asymptotes, see here: http://socratic.org/questions/what-is-a-vertical-asymptote-in-calculus?