For a real number x, find the number of different possible values of x/|x|.
If x is positive, \(x \over | x |\) will always equal 1.
If x is 0, \(0 \over 0 \) will equal undefined
If x is negative, \(x \over | x |\) will equal -1.
Thus, there are \(\color{brown}\boxed{3}\) distinct values.