The last one is a dependent clause because you can make two separate sentences out of it :)
To introduce what the paragraph is going to be about
To inspire Telemachus to stand up for himself.
The story of Agamemnon is of a man who commanded the United Greek Armed forces in the Trojan War. But he was killed once he arrived home. This relates to the dilemma that Telemachus was in as the suitors stated they would kill him once he arrived.
Hope this helps!