This work investigates the behavior of the orbit transfer switching function (SF). Recent work indicated that use of an analytical expression for the SF could significantly reduce the computational time required to determine the coast arcs during trajectory optimization This work includes a more detailed analysis of the SF during coasting. In addition to considering how the primer vector and SF in various coordinate systems are related, analytical expressions that are valid during coasting are derived for both in terms of two different systems that can then be related to many others. Also, derivatives of the SF in both coordinate systems are derived. Given that the SF during such coast arcs can manifest multiple frequencies simultaneously, some possible behaviors of such functions are considered relative to finding bounds for a zero finding algorithm (ZFA). An improved method for finding bounds is proposed which involves calculating the derivative of the SF. Calculations are done which indicate that the derivations are correct. Examples are presented for which the proposed method enables the optimal solutions to be found.