We probe the transition to bistability that exists in a hybrid metal nanoparticle and semiconductor quantum dot (SQD) system when they are strongly coupled. In particular, we see a discontinuous jump in the response of the system (in both the diagonal and off-diagonal density-matrix elements) and a SQD response that is highly suppressed above resonance in this transition region. This discontinuous response and suppression arise because the SQD acts as a driven (quantum) oscillator. The phase change at resonance drastically alters the hybrid response when crossing the resonance. The study of this transition region, the discontinuity, and the suppression phenomena provides different insights into understanding this system, predicts a more complicated behavior than previously thought and corrects earlier work where the transition region was absent.