Yes, The Hunger Games uses compound sentences.
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In the beginning of her private training session, it mentions that when she picks up the bow, she finds that the Capitol's bows don't pull back as far as the one she uses does and needs to adjust to that. In the beginning of the Hunger Games, the Gamemakers set out a silver colored bow with a sheath of arrows to tempt her into the Cornucopi. Later in the Hunger Games, after Katniss drops the bee's nest on the Careers, she retreives the bow and arrows from Glimmer's dead body, who was the one that grabbed it at the Cornucopia. I hope that helped :)
She uses it as a tourniquet for Peeta's bad leg. She then frees it from the torniquet, with Peeta's permission, and uses it in sympathy to put Cato out of his misery and end his life.
The Hunger Games address reality television and the public's obsession with it, and how dangerous or silly it can be to all parties participating in the viewing, and performing. The Hunger Games also addresses human rights and freedoms with the creation of the 13th district. It emphasizes that people can rebel against a government for their rights.
The Hunger Games is actually considered Dystopian fiction. It is also Science fiction because it takes place in the future, they have more technology, and it is still the future of OUR universe, just with a different name. So out of the three I'd have to go with Science fiction.