Final answer:
The subcellular structures that perform specific functions without being enclosed by their own membrane are ribosomes and centrioles. Ribosomes are essential for protein synthesis, and centrioles are involved in cell division.
Step-by-step explanation:
The subcellular structures that perform specific functions but are not enclosed in their own membrane are ribosomes and centrioles. Therefore, the correct answer to the student's question is C) Ribosomes / Centrioles. While many other organelles are surrounded by membranes and are part of the endomembrane system, such as the Golgi apparatus, endoplasmic reticulum, lysosomes, and peroxisomes, ribosomes and centrioles are not.
Ribosomes are responsible for protein synthesis and can be found either floating freely in the cytoplasm or attached to the rough endoplasmic reticulum. Centrioles play a crucial role in cell division in animal cells by facilitating the organization of the mitotic spindle. Both structures are essential for cellular function but lack the phospholipid bilayer membrane that characterizes many other cellular organelles.