Final answer:
Proteins synthesized on free ribosomes typically remain in the cytoplasm to perform their functions and do not pass through the Golgi apparatus.
Step-by-step explanation:
Proteins that are synthesized on free ribosomes in the cytoplasm generally remain in the cytoplasm and perform their functions locally; they do not typically go through the Golgi apparatus. Unlike proteins synthesized by bound ribosomes, which are destined for secretion or for incorporation into cell membranes or organelles, the proteins made on free ribosomes usually serve functions within the cytosol of the cell. Therefore, the correct answer to what happens to these proteins is that they remain in the cytoplasm and function locally, corresponding to option c.