Answer
Check work for discussion.
Work Step by Step
The function has an infinite number of discontinuities. The discontinuities are at $x=n$ where $n=...-3, -2, -1, 0, 1, 2 ,3...$ ( n is an integer.)
Note: Usually to check if a number is an integer or not, it is compared to a floor or ceiling function (the greatest integer function is a floor function).
For example, if $z$ is not an integer, then $z\ne[[z]].$
