What are the general properties of postsynaptic potentials?

Postsynaptic potentials are graded potentials. They vary in magnitude depending on the amount of the neurotransmitter released and the number of receptors activated. Postsynaptic potentials occur locally at the synapse and decrease in strength as they diffuse away from the site of origin. 

Postsynaptic potentials can either initiate action potentials by depolarizing the membrane or inhibit action potentials by hyperpolarizing the membrane.