We introduce bloomRF as a unified method for approximate membership testing that supports both point- and range-queries. As a first core idea, bloomRF introduces novel prefix hashing to efficiently encode range information in the hash-code of the key itself. As a second key concept, bloomRF proposes novel piecewise-monotone hash-functions that preserve local order and support fast range-lookups with fewer memory accesses. bloomRF has near-optimal space complexity and constant query complexity. Although, bloomRF is designed for integer domains, it supports floating-points, and can serve as a multi-attribute filter. The evaluation in RocksDB and in a standalone library shows that it is more efficient and outperforms existing point-range-filters by up to 4x across a range of settings and distributions, while keeping the false-positive rate low.