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AMC10 2027 - Self-practice Set 4 Question 14

AMC10 · AMC10 2027 - Self-practice Set 4

Question 14

Let $f(x)=\lfloor|x|\rfloor-|\lfloor x\rfloor|$ for every $x\in\mathbb R$. What is the range of $f$?
  1. $\{-1,0\}$
  2. $\mathbb Z\setminus\mathbb N$
  3. $\{-1,0,1\}$
  4. $\{0\}$
  5. $\mathbb N$