
Ed M. answered 01/15/16
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The answer depends on how you punctuate the sentence under the standard conventions, and you have three principal options (and indeed one of these must be chosen to make your sentence anywhere near "correct"):
- The girl had been upset. Yet now she smiled and told us about her day.
- The girl had been upset; yet now she smiled and told us about her day.
- The girl had been upset, yet now she smiled and told us about her day.
That is, yet can function as either a conjunctive adverb as in 1. and 2. or a coordinating conjunction as in 3. A conjunctive adverb joins two independent clauses, which may be punctuated as separate sentences (as in 1.) or joined by a semicolon (2). In both cases, however, it's the internal structure of the clauses themselves that determines the overall status as simple, compound or complex, and here both clauses are simple since there is no other coordination nor subordination. For example, if the first sentence of 1. were While she walked home, the girl had been upset, this would be complex since you have an independent clause (the girl had been upset) joined to a dependent or subordinate clause (While she walked home). But if the first sentence of 1. were The girl had been upset and she cried all the way home, this would be compound since it consists of two independent clauses joined by the coordinating conjunction and. (independent because both these clauses could be written separate sentences). This same analysis could be applied to sentence 2. but with slightly different terminology since technically 2. is a single written sentence.
Similarly, as noted above yet can be used like and, i.e., as a coordinating conjunction, as it is in option 3., which is a compound sentence consisting of the two independent clauses The girl had been upset and (yet) now she smiled and told us about her day. And if we were to add a dependent clause to this sentence, e.g., While she walked home, [the comma could also be omitted here] the girl had been upset, yet now she smiled and told us about her day, the result would be a compound-complex sentence since you'd have a compound sentence in which at least one of the independent clauses contains a dependent clause as well.