That depends on your initial assumptions, which you can shape over time (though you may not want to or find it advantageous to do so).
>some times people are having a really bad day for reasons you can't see and a little bit of empathy goes a long way
I don't see how you can have much empathy. Patience, yes. Compassion, yes. Full sharing of feelings, no, purely by the description of the scenario.
"Sympathy (from the Greek words syn "together" and pathos "feeling" which means "fellow-feeling") is the perception, understanding, and reaction to the distress or need of another human being."[0]
"When you sympathize with someone, you have compassion for that person, but you don’t necessarily feel her feelings."[1]
Generally the difference between empathy and sympathy is the internal response to the feelings of others. If you personally are feeling the same thing as the person, then that's generally empathy, otherwise it's generally sympathy.
define pity
pit·y
ˈpidē/
noun
noun: pity
1.
the feeling of sorrow and compassion caused by the suffering and misfortunes of others.