2004 Nissan 350Z • 133 miles

Just bought a 2004 Nissan 350z with 133K on it. Just curious as it is automatic transmission and my question is, is it normal that when your driving off in drive that you don't really feel the traditional shift into gears. It seems to early on but almost just stays in a steady gear. Is that just the way the car drives normally? Hopefully, I am making sense on my question!
December 29, 2012.

That transmission and engine really take a lot of "learned" tuning by the way the driver operates it. It depends a lot on throttle position and how hard you drive it, if it is stop and go ro HQWY, etc.
So, it will do a lot of odd things when you drive it differently especially in a situation where the differential may be slipping a lot more than usual. I would not worry about it.