# What is the range of the function y = tan x?

##### 1 Answer
Sep 6, 2014

The range of the tangent function is all real numbers! If you look at the graph below:

you will see that the various repeated "pieces" of the graph point both upward and downward in an increasing direction from left to right. The function is undefined at $\frac{\pi}{2}$ and its odd multiples, or $\frac{\left(2 n + 1\right) \pi}{2}$ .
Therefore, infinity and negative infinity describe where this function graph is heading.....that is what we call "all real numbers".