The classic Banach-Stone Theorem establishes a form for surjective, complex-linear isometries (distance preserving functions) between function spaces. Mathematician Takeshi Miura from Niigata University questioned what could be said about surjective, real-linear isometries after finding a counter-example that demonstrated the shortcomings of the Banach-Stone Theorem to classify such functions. Through a careful examination of the Banach-Stone we found why the theorem does not hold in general and proved a theorem that gives a form for real-linear isometries between function spaces.