Give two specific signals that move through the symplast, and describe the function of each signal

Two examples are auxins and abscisic acid. The former is responsible for the apical growth of plants while the latter promotes dormancy / inhibits growth.

Symplast transport involves transport through the living protoplasm of the plant's cells. This is unlike in the apoplast that is the passive movement in the extracellular spaces within the plant cells. Plant signaling molecules pass through the symplast system such us in the plasmodesmata.