Answer
Continuous for all real numbers except $\dfrac{\pi (2n+1)}{2}$, where $n$ represents an integer.
Work Step by Step
We know that the tangent function is undefined for $\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2}$. That is, for $\dfrac{\pi (2n+1)}{2}$, where $n$ represents an integer.
Therefore, it is continuous everywhere, except for $\dfrac{(2n+1)}{2}\pi$, where $n$ represents an integer.
