If X is between -3 and -1, and Y is between -1 and 1, then X² - Y² is in between which of the following?

1. **Analyze X**: The question states X is 'between' -3 and -1 [18]. Since X is negative, when we square it, the order flips. (-3)² is 9 and (-1)² is 1. So, X² is strictly between 1 and 9.\n\n2. **Analyze Y (The Trap)**: Y is between -1 and 1. This range includes the number 0. If we just squared the endpoints, we would get 1 and 1, which doesn't make sense for a range. We must recognize that as Y goes from -1 to 0 to 1, Y² goes from 1 down to 0 and back up to 1. Thus, the minimum value of Y² is 0 [15]. Range of Y² is [0, 1).\n\n3. **Calculate X² - Y²**: We use the 'Min/Max Logic' [16].\n - To get the **Largest** result: Take the Largest X² and subtract the Smallest Y².\n -> 9 (Max X²) - 0 (Min Y²) = 9.\n - To get the **Smallest** result: Take the Smallest X² and subtract the Largest Y².\n -> 1 (Min X²) - 1 (Max Y²) = 0.\n\n4. **Conclusion**: The result lies between 0 and 9. Checking the options, Option D is the only one that matches this range.