Step 1: Recall the three regulatory regions of the lac operon.
The promoter is where RNA polymerase attaches, the operator sits right next to it, and the regulator gene simply codes for the repressor protein itself.
Step 2: Think about what switching off the operon needs.
To stop transcription, the repressor has to physically block RNA polymerase from moving forward along the DNA.
Step 3: Identify where that blocking happens.
The repressor achieves this by attaching to the operator sequence, sitting in the path of RNA polymerase.
Final answer: Option 2, Operator.