Answer
Mutations in the promoter sequence prevent RNA polymerase from binding and transcribing the operon; this results in no expression.
Binding of the CAP protein (bound to cAMP) to the CAP-cAMP binding site facilitates the binding of RNA polymerase to the promoter sequence. Mutations in the gene that encodes the CAP protein or in the CAP-cAMP binding site make binding of RNA polymerase to the promoter less likely. This results in a lower than normal expression of the operon.
Loss of function mutations in the repressor protein or in the operator region to which it binds prevent the repressor from blocking transcription. This results in constitutive expression of the operon.
Gain of function mutations in the gene for the repressor (super-repressor) cause the repressor to bind to the operator even in the presence of lactose; this results in no expression.
Mutations in the lacZ gene which encodes beta-galactosidase result in no expression of beta-galactosidase.