Question

What purpose does the semicolon serve in the following sentence?

Answer 1

The purpose of the semicolon in the example is to join two related independent clauses (option B)

In this case, the semicolon is used instead of a conjunction. They are generally related however, the second part might not be an explanation or clarification. 
the semicolon could have been replaced by BECAUSE perfectly well. 

- Leticia has to leave early this afternoon because she has a doctor's appointment.

Answer 2

I think the answer would be B, since both sentences in this one are both independent clauses, and the semicolon separates them.