  We demonstrate tuning of interactions between fermionic 40K and bosonic 87Rb
atoms by Feshbach resonances and access the complete phase diagram of the
harmonically trapped mixture from phase separation to collapse. On the
attractive side of the resonance, we observe a strongly enhanced mean-field
energy of the condensate due to the mutual mean-field confinement, predicted by
a Thomas-Fermi model. As we increase heteronuclear interactions beyond a
threshold, we observe an induced collapse of the mixture. On the repulsive side
of the resonance, we observe vertical phase separation of the mixture in the
presence of the gravitational force, thus entering a completely unexplored part
of the phase diagram of the mixture. In addition, we identify the 515 G
resonance as p-wave by its characteristic doublet structure.
