where can I check when I purchased or bought my iphone?

If you have Verizon, in the "My Verizon" app, tap the 3 (mine are red) bars in upper left corner, scroll down to my devices & tap it, scroll down to My orders & tap that, and that will tell you when you purchased your device. Or you can just call your provider or the store where you bought the phone & they can tell you. The My Verizon app is a free app. If you don't use Verizon, maybe your phone service offers something similar?

If you did not keep any of the original information, you could try contacting the place where you purchased it to see if they can find anything in their records.