Determining Functional and Transitive dependencies from Relational Model (with no sample data)
You are being asked to engage in reverse engineering.  Reverse engineering is often done in the case of legacy systems, in order to find out what goals the original designers might have been pursuing.  It's really an iffy proposition, nevertheless.  You best handle is the foreign key constraints.  These reveal the FDs, presumably.  Also, you can presume that every non key value is dependent on the primary key of the table it is in.

In regular (forward) engineering, you don't discover the FDs by studying the design.  You study the subject matter, and uncover the FDs there.  This can be time consuming, and people driven by a tight schedule may accuse you of "analysis paralysis".  Only once you've discovered the FDs, among other subject matter features, and you've decided whether or not to pursue a normalized design, do you proceed to compose the tables and the constraints.

Good luck.  You're going to need it.