When you "sweep" a private key, how are all the addresses which it controls discovered?

It doesn't seem like it would be feasible to test every UTXO to see if it belongs to a key. But I don't know the math.Edit: the challenge is that every private key controls many public keys. Or is this a misconception and only true of HD keys.Does this also mean a change address is under the control of a new private key?I am mainly trying to understand how a wallet.dat backup or 12 word seed can be used to recover funds from many addresses. via /r/Bitcoin http://bit.ly/29c9nXo