What describes the domain of y=tanx, where n is any integer?

Assuming you meant "where x is any integer":

[tex]\tan{x}[/tex] is defined as [tex] \frac{\sin{x}}{\cos{x}} [/tex], so it would be defined for every value of [tex]x[/tex] except for those where [tex]\cos{x}=0[/tex], which is true when [tex]x= \frac{\pi}{2} +2\pi k[/tex] and [tex]x= \frac{3\pi}{2} +2\pi k[/tex], where [tex]k[/tex] is some integer. These values of [tex]x[/tex] where [tex]\tan{x}[/tex] is undefined are both irrational; they cannot be expressed as a ratio between two integers, and so limiting the domain to integers makes sure that we'll skip over those points every time as [tex]x[/tex] is increasing.

So, the domain of [tex]y=\tan{x}[/tex], when limiting that domain to the integers, is the set of all integers, [tex]\mathbb{Z}[/tex].