The graph between the input voltage ($V_i$) and the output voltage ($V_o$) of a transistor connected in common emitter configuration is shown in the figure. The active, saturation and cutoff regions of the transistor are respectively
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For a CE transistor switch:
Low Input ($V_i$ low) $\rightarrow$ OFF state $\rightarrow$ Cutoff Region (High Output $V_o$).
High Input ($V_i$ high) $\rightarrow$ ON state $\rightarrow$ Saturation Region (Low Output $V_o$).
The steep transition part in between is the Active Region, used for amplification.
