Atomic force microscopy (AFM) images of graphene and graphite show contrast with atomic periodicity. However, the contrast patterns vary depending on the atomic termination of the AFM tip apex and the tip-sample distance, hampering the identification of the atomic positions. Here, we report quantitative AFM imaging of epitaxial graphene using inert (carbon-monoxide-terminated) and reactive (iridium-terminated) tips. The atomic image contrast is markedly different with these tip terminations. With a reactive tip, we observe an inversion from attractive to repulsive atomic contrast with decreasing tip-sample distance, while a nonreactive tip only yields repulsive atomic contrast. We are able to identify the atoms with both tips at any tip-sample distance. This is a prerequisite for future structural and chemical analysis of adatoms, defects, and the edges of graphene nanostructures, crucial for understanding nanoscale graphene devices.