the operator's function is to act as a regulatory element that helps control the expression of the lac operon in response to the presence or absence of lactose.

The operator in the lac operon is a segment of DNA located between the promoter and the genes coding for the enzymes involved in lactose metabolism (lacZ, lacY, and lacA). It serves as a binding site for the lac repressor protein.

When lactose is absent, the lac repressor binds to the operator, preventing RNA polymerase from transcribing the lac genes. This ensures that the enzymes necessary for lactose utilization are not produced when lactose is not available.

In the presence of lactose, some of it is converted to allolactose, which acts as an inducer by binding to the lac repressor. This binding causes a conformational change in the repressor, resulting in its release from the operator. As a consequence, RNA polymerase can access the promoter and transcribe the lac genes, leading to the production of the enzymes required for lactose metabolism.

This regulatory mechanism allows the cell to efficiently manage energy resources by only expressing the genes for lactose metabolism when lactose is present, thus illustrating a key example of gene regulation in prokaryotes.