Graph-based function models used in early-stage systems design usually represent only one operational mode of the system. Currently there is a need but no rigorous formalism to model multiple possible modes and states of a device in the same model and to perform model-based reasoning with that information such as predicting state transitions or causal propagations. This paper presents a formal representation of operational modes and states of technical devices 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, grammar rules, and application of each verb in modeling is illustrated. Finally, the representation is validated by implementing it on a graphical function modeling tool and using it to illustrate the verbs' modeling and reasoning ability for predicting mode and state transitions in response to control signals and cause-and-effect propagation throughout system-level models.