Answer: The word in bold ("before") is being used as a (A.) subordinating conjunction.
Explanation: A subordinating conjunction is word used to introduce a dependent clause, that is to say a clause that cannot stand alone as a sentence. In the sentence "Alex always does warm-up exercises before he begins jogging", "before" is a subordinating conjunction because it is introducing the dependent clause "before he begins joggins". Moreover, "before" is joining the independent clause "Alex always does warm-up excercises" to the dependent clause previously mentioned.
