Voltage Rating of a device
If I heard something was "rated for 3V", I would try to avoid exceeding that voltage. "Rating" refers to a safe boundary, and that boundary is usually a maximum - things are more likely to break from too much power than too little. If the buzzer did not work just below 3V, then one might risk going just above.

The input range is the range of values for which the device will operate correctly. Going below 3V is unlikely to cause any problems except (temporary) silence. Supplying a higher voltage closer to the middle may result in better operation, and everything will be fine up to 10V. The 10V need not be the upper safe boundary, though the absolute maximum will usually be somewhere close to the upper limit of the input range. Exceeding that increases the risk of loud buzzing being replaced by (permanent) silence.