# What is the vertical asymptote of 1/x?

##### 1 Answer
Aug 24, 2014

The vertical asymptote of $\frac{1}{x}$ 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 $\pm \infty$. Thus, in the example above, we look for when the function $f \left(x\right) = \frac{1}{x}$ approaches $\pm \infty$.

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?