The function $\lfloor x\rfloor$ is defined as the largest integer less than or equal to $x$. For example, $\lfloor 5.67\rfloor = 5$, $\lfloor -\tfrac 14\rfloor = -1$, and $\lfloor 8\rfloor = 8$. What is the range of the function $$f(x) = \lfloor x\rfloor - x~?$$Express your answer in interval notation.
