Range

The given expression is . The absolute value function is minimized when , since the absolute value of a number is always non-negative, and the minimum occurs when the number inside the absolute value is zero.
Thus, for : For values of within the given range , increases, leading to smaller values of .
Therefore, the maximum value of in the given range is , which occurs when .

Step 1: Understand the Greatest Integer Function The greatest integer function returns the largest integer less than or equal to .
For example:
Step 2: Evaluate for Each Element in the Domain The domain of is . We evaluate for each element in the domain:
1. For : (Since is the greatest integer less than or equal to .)
2. For : (Since is the greatest integer less than or equal to .)
Step 3: Determine the Range The range of is the set of all output values of . From Step 2, the outputs are and .
Therefore, the range is:
Step 4: Verify the Answer The range corresponds to option (D).
Final Answer: The range of is:
Thus, the correct option is (D).