Auto transmission/Not sure if a problem
 

I bought a used 2003 Sonata V6 auto trans. My first Hyundai and first foreign auto transmission.Not only does it seem to shift frequently, it shifts "hard" or more noticable than my US transmissions, but my main concern is that if Im in 4th gear at a higher speed (greater than40) and the transmission downshifts to 3rd because I am accellerating to pass or going up a hill, it doesnt shift back into 4th easily. Some times I have to let off the accellerator completely and drift for a few seconds then it will shift into 4th again and sometimes I'll have to manually put it in fourth by switching over to the 'semi auto' mode. Does anyone know if this is normal for the Hyundai or might there be a problem. I dont have any check engine lights on. Thnanks in advance.
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