Software testing can benefit from technologies that enable evolution toward increased engineering discipline. In current practice, software developers lack practical means to determine the full functional behavior of programs under development, and even the most thorough testing can provide only partial knowledge of behaviors. Thus, effective scientific principles and engineering technology for revealing software behavior should have a positive impact on software testing. This paper describes the emerging technology of function extraction (FX) for computing the behavior of programs to the maximum extent possible with mathematical precision. We explore how the use of FX technologies can transform methods for functional verification of software. An example illustrates the value of full behavior knowledge for complete and confident assessment of software function and fitness for use. We conclude by describing a transition strategy for introducing FX technology into the development and operation of software systems.