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