Final answer:
The posterior pituitary releases vasopressin, along with oxytocin, but does not synthesize them, as they are produced by the hypothalamus. The anterior pituitary, on the other hand, produces several hormones including tropic hormones like FSH and LH.
Step-by-step explanation:
The posterior pituitary gland is best known for the storage and release of certain hormones, namely antidiuretic hormone (ADH), also known as vasopressin and oxytocin. These hormones are not synthesized in the posterior pituitary but are produced by neurons in the hypothalamus. They travel down axons to the posterior pituitary where they are stored until they are released into the bloodstream. Hence, the correct answer to the student's question is (a) releases vasopressin.
The other options provided in the question pertain to functions of the anterior pituitary or other structures and thus are not accurate in describing the posterior pituitary's role. For example, the anterior pituitary produces tropic hormones, which include thyroid-stimulating hormone (TSH), adrenocorticotropic hormone (ACTH), follicle-stimulating hormone (FSH), and luteinizing hormone (LH).
It is important to note that while the posterior pituitary does release hormones, it does not produce them, and it definitely does not release hormones like growth hormone (GH), LH, FSH, or hormones regulated by signals from the islets of Langerhans.