Cut-off Region: -
The transistor is off. There is no conduction between the drain and the source when the gate-source voltage is greater than the cut-off voltage (ID = 0 for VGS > VGSoff)
The transistor is on. The drain current is controlled by the gate-source voltage (VGS) and relatively insensitive to VDS. In this region the transistor can be an amplifier.
In the active Region ID = IDSS (1 – VGS / VGSoff) 2
Ohmic Region: -
The transistor is on, but behaves as a voltage proportional to the source-drain voltage and is controlled by the gate voltage.
ID = IDSS [ 2 (1 – VGS / VGSoff) VDS / - VGSoff - (VDS / VGSoff) 2 ]
In the Ohmic Region: RDS ≈ VGSoff / 2IDSS (VGS - VGSoff) = 1 / gm