What is the value of (f(x)=\lfloor x \rfloor) on the interval (2\le x<3)?

Correct answer: (2)

The floor function \(\lfloor x\rfloor\) gives the greatest integer less than or equal to \(x\). For every number in the interval \(2\le x<3\), the greatest integer not exceeding that number is 2. This includes the left endpoint \(x=2\), where the value is exactly 2, but excludes \(x=3\), where the value would become 3. Therefore option A is correct.

For instance, \(\lfloor2\rfloor=2\), \(\lfloor2.4\rfloor=2\), and \(\lfloor2.99\rfloor=2\). Thus the function remains constant at 2 throughout the stated interval, so its graph is a horizontal segment at height 2. Option B would apply at \(x=3\), but that endpoint is not included.