A multi-function apparatus which is capable of properly coping with cases where an auto-clear function is activated to thereby improve operability after execution of the function. The operating section of a copying machine displays an operating screen associated with each function and receives inputs via the operating screen. According to the auto-clear function, set values associated with predetermined functions are reset to initial values when no input operation has been performed via the operating section over a predetermined time period, and the operating section is caused to display an operating screen associated with a predetermined function. A controller unit of the machine determines whether the copying machine should be operated in a first mode in which disconnection from the network is carried out or in a second mode in which connection to the network is maintained. The controller unit selects one of the first mode and the second mode based on a result of the determination.