Graph-based function models used in early-stage systems design usually represent only one operational state and mode of the system. Currently, there is a need, but no rigorous formalism to model the different modes in the function model and logically predict the effects of the system transitioning between the modes. This paper presents a representation of operational modes and states of technical systems based on automata theory for both discrete and continuous state transitions. It then presents formal definitions of three signal-processing verbs that actuate or regulate energy flows: Actuate_E, Regulate_E_Discrete, and Regulate_E_Continuous. The graphical templates, definitions, and application of each verb in modeling is illustrated. Finally, a system-level model is used to illustrate the verbs’ modeling and reasoning ability, in terms of cause-and-effect propagation and the systems’ transition between operational modes.