It is not very hard to fake righteousness and authenticity if one really sets their mind to it. Jesus knows the hearts of many of the people gathered around him though, and thus preaches to them again.
"Beware of practicing your righteousness before men to be noticed by them; otherwise you have no reward with your Father who is in heaven. When therefore you give alms, do not sound a trumpet before you, as the hypocrites do in the synagogues and in the streets, that they may be honored by men. Truly I say to you, they have their reward in full. "But when you give alms, do not let your left hand know what your right hand is doing, that your alms may be in secret; and your Father who sees in secret will repay you (Matthew 5:1-4)."
Right after Jesus sets the standard for the behavior of a Christian in Matthew 5:13-48, he emphasizes authenticity in Matthew 6:1-18. It isn't good enough to live the right way, Jesus calls the people to to authentic living. It's not the kind of goodness that can come from anyone who doesn't have God living in them. He calls for something that is genuine.
Jesus contrasts self-righteousness, the kind that we can do on our own without God, and the righteousness that God brings. He also contrasts the way that the Pharisees pray and the way that they should pray. When Jesus tells the people to "not sound a trumpet," he means for them not to show off when they pray, when they give alms, and when they humble themselves.
In Luke 21:1-4 Jesus and his disciples see a widowed woman putting the last of her little money into the offering meekly, while those around her dropped their gold coins in order to show off their opulence. Jesus told his disciples that the widow had given more than those who were putting in the gold because she had given all of her money, and that she had done it in a humble spirit before God rather than before men.
Jesus also tells the people not to be showy about their fasting. Fasting is supposed to be a time when the person puts aside food and puts aside the time that they would spend eating food to pray and spend time with God. Jesus doesn't say that all fasting is bad. If there is a good reason to fast, then keep it between you and the Lord, because having a hunger strike for AIDS won't change anything.
In all of these things, Jesus tells the people that they are not to live their lives to impress other people. They are to live it out of devotion to the Lord.
