nt.number theory – rank 1 evaluations which are not discrete on finite transcendental extensions of rationals

assume $ K = mathbb {Q} (X_1, dots, X_n) $ is a purely transcendental extension of rationals on an infinitely indeterminate number. Can anyone give an example of rank $ 1 $ evaluation on $ K $ who fails to be discreet?

If not, is there a theorem which shows that such a rank $ 1 $ should the assessment be discreet?