State Function:
 In thermodynamics, a state function, state quantity, or a function of the state, is a property of a system that depends only on the initial and final state the system, not on the way in which the system acquired that state.
 A state function describes the equilibrium state of a system and thus also describes the types of system.
 The cyclic integral involving a state function is always zero.
 All the thermodynamics property satisfy the requirements of state function.

∆U = q + w change in thermodynamic energyS = q_{rev}/T entropyH = U = PV enthalpyG = H – TS Gibb’s free energyA = U – TS Helmholtz free energy

Internal energy, enthalpy, entropy are the example of state functions.
Path Function:
 Path function depends on the path taken to reach that specific value, not on the initial and final state of that value.
 Path function needs multiple integral and limits of the integration in order to integrate.
 It is based on how the state of a system was established.
 Work, heat, arc length are the example of path function.