The function f is defined by

f(x)=\lfloor|x|\rfloor-|\lfloor x\rfloor|

for all real numbers x, where \lfloor r\rfloor denotes the greatest integer less than or equal to the real number r. What is the range of f ?

**Answer Choices**

A. \{-1,0\}

B. the set of nonpositive integers

C. \{-1,0,1\}

D. \{0\}

E. the set of nonnegative integers