In the context of the function \( h(m) \), which represents the number of helium balloons a machine can blow up per minute, the appropriate domain would be:
All positive integers
This is because the number of balloons blown up per minute cannot be negative, and since we are dealing with a count of balloons, it should also be a whole number (integer). Thus, the domain consists of all positive integers (1, 2, 3, ...).