Certification authorities also manage, distribute, and store certificates and certificate revocation lists. It is computationally infeasible to find any two distinct inputs that map to the same output. Posession of such a key enables access to all data encrypted with that key for the lifetime of its use. A long-term encryption key can be contrasted with a session key. The two keys have the property that, given the public key, it is computationally infeasible to derive the private key.
Some algorithms can perform all three functions and some can perform only one.
In this instance, the symmetric key would likely be encrypted with the recipient's public key to facilitate key exchange.