Final answer:
Eukaryotic RNA polymerase I's function is to transcribe rRNA genes, which are crucial for the formation of ribosomes required for protein synthesis in the cell. This polymerase works with transcription initiation factors to elongate the rRNA transcript.
Step-by-step explanation:
The function of eukaryotic RNA polymerase I is the transcription of rRNA genes. This is a critical process in the synthesis of ribosomes, which are essential for protein production in the cell. RNA polymerase I binds to an upstream promoter along with transcription initiation factors, and once initiated, it catalyzes the formation of phosphodiester bonds, elongating the transcript for the formation of ribosomal RNA (rRNA).
Ribosomal RNAs are the most abundant and form the structural and functional components of the ribosomes. Although mRNA is synthesized in greater variety, rRNA makes up the bulk of RNA within a cell. It's important to note that, unlike RNA polymerase II which transcribes mRNA genes, and RNA polymerase III which transcribes both rRNA and tRNA genes, RNA polymerase I is specifically dedicated to rRNA gene transcription.