Plotting amplifier transfer characteristics
This plot looks like a reasonable way to estimate transfer function.

Power Amps tend NOT to run in Class A unless they are RF, so the transfer function of each polarity signal is different with crossover design to merge and least amount of negative feedback to reduce distortion and extend bandwidth 

But to design for better linearity, we need circuit details to ensure;


bias current sink/source exceeds load current and 
output swing stays 2V away from saturation.
analyze non-linear loads