  Inspired by the original definition of mock theta functions by Ramanujan, a
number of authors have considered the question of explicitly determining their
behavior at the cusps. Moreover, these examples have been connected to
important objects such as quantum modular forms and ranks and cranks by Folsom,
Ono, and Rhoades. Here we solve the general problem of understanding
Ramanujan's definition explicitly for any weight $\frac12$ mock theta function,
answering a question of Rhoades. Moreover, as a side product, our results give
a large, explicit family of modular forms.
