If \(f(x)=\lfloor 2x\rfloor\) for \(x\in[0,2)\), what is the range of \(f\)?

Correct answer: \(\{0,1,2,3\}\)

Since \(x\in[0,2)\), we have \(2x\in[0,4)\). Therefore, the possible integer values of \(\lfloor 2x\rfloor\) are \(0,1,2,3\), and each of them is attained. For example, the value is \(0\) when \(x\in[0,\tfrac12)\), \(1\) when \(x\in[\tfrac12,1)\), and so on. The endpoint \(x=2\) is excluded, so \(2x=4\) and the value \(4\) cannot occur; hence option B is incorrect. Thus, the range is \(\{0,1,2,3\}\). Exam tip: For the greatest-integer function, check carefully whether the endpoints of the input interval are included.