Final answer:
Transcription factors that bind to DNA and suppress gene transcription are known as repressors. In this case, since the gene transcription becomes undetectable after binding of the transcription factor, it is exhibiting a repressor function.
Step-by-step explanation:
If a transcription factor binds to DNA near a gene and causes transcription of that gene to become undetectable, it is functioning as a transcriptional repressor. Repressors are proteins that bind to specific DNA sequences within the regulatory region to suppress transcription. These regulatory regions include promoters, operators, and in some cases, enhancers, although enhancers are generally associated with the activation of transcription. This binding can inhibit the binding of RNA polymerase to the DNA or the progression of RNA polymerase, thereby blocking transcription from occurring.
In this particular case, when the transcription factor binds and transcription becomes undetectable, it is performing a repressor function. Therefore, the correct answer to the question is c) Repressor function.