You will be told at check-in whether your bags are being checked all the way through or not (and if you're not, ask!). You should also check on both the baggage tag as they put it on your bag, as well as on the receipt that they give you, that the final destination airport it listed.
The exception to this rule is locations where all passengers need to collect their baggage, which includes (almost all) international flights INTO the US. In this case, even though the bags are technically checked all the way through to the destination, you still need to collect them on entry to the US so that you can carry them yourself through customs. This will not affect your trip out of the US, but if you are returning on a similar route then you WILL need to collect your bags at your first point of entry into the US.
As you are booked on a single ticket your bags should be checked all the way through - but it's always a good idea to make sure at check-in just in case...