Hi dleone11,
If you purchased a preowned iPhone from AT&T, the warranty will continue from the date the original owner activated it.
You can purchase the AppleCare Protection Plan for any iPhone within the one-year hardware warranty, as long as its available in your country. This webpage:
http://www.apple.com/support/products/applecareiphone.html provides more information about the AppleCare Protection Plan for the iPhone.
You can contact AppleCare to get more information about your iPhones warranty or purchase the AppleCare Protection Plan.
U.S. iPhone technical support: 1-800-MY-IPHONE (1-800-694-7466)
-Jason