graded potentials develop in the dendrites that influence the generation of an action potential in the axon of the same cell.

This is called a generator potential. 

Depolarization in a postsynaptic potential is called an excitatory postsynaptic potential (EPSP) because because it causes the membrane potential to move toward threshold. 

Hyperpolarization in a postsynaptic potential is an inhibitory postsynaptic potential (IPSP) because it causes the membrane potential to move away from threshold.