Determining whether a textual phrase denotes a functional relation (i.e., a relation that maps each domain element to a unique range element) is useful for numerous NLP tasks such as synonym resolution and contradiction detection. Previous work on this problem has relied on either counting methods or lexico-syntactic patterns. However, determining whether a relation is functional, by analyzing mentions of the relation in a corpus, is challenging due to ambiguity, synonymy, anaphora, and other linguistic phenomena. We present the LEIBNIZ system that overcomes these challenges by exploiting the synergy between the Web corpus and freelyavailable knowledge resources such as Freebase. It first computes multiple typed functionality scores, representing functionality of the relation phrase when its arguments are constrained to specific types. It then aggregates these scores to predict the global functionality for the phrase. LEIBNIZ outperforms previous work, increasing area under the precisionrecall curve from 0.61 to 0.88. We utilize LEIBNIZ to generate the first public repository of automatically-identified functional relations.