Final answer:
In the given sentence, 'while' and 'as' are the subordinating conjunctions, as they introduce subordinate clauses, whereas 'but' is a coordinating conjunction connecting two independent clauses.
Step-by-step explanation:
The student is tasked with identifying subordinating conjunctions within the provided sentence. In English grammar, a subordinate clause is a clause that provides additional information to the main clause but cannot stand alone as a complete sentence. A subordinating conjunction is a word or phrase that links a subordinate clause to the main clause. The sentence given by the student includes two subordinating conjunctions from the options provided: 'while' and 'as'. Thus, the sentence 'You may explore broad academic fields and intellectual interests while you pursue your college degree, but you should develop a good sense of your chosen career as your studies become more focused.' has 'while' and 'as' playing the role of subordinating conjunctions. On the other hand, 'but' is a coordinating conjunction, which is used to connect two independent clauses.