Take another look at the passage:
Emily pounded on the bedroom door, demanding a little quiet so that she could study for her physics midterm. Her sister Amy ignored the request. And continued banging on the drum set that she bought at a garage sale.
You chose the first part, Emily pounded on the bedroom door, demanding a little quiet .... This part has a main clause: Emily is the subject; pounded is the verb. A fragment will not have a main clause.