Faith has two components, call them A and B. A offers something, and B either responds or does not. A man hanging by his fingertips from the edge of a cliff sees a withered plant within reach. He offers his grip to that plant, and the plant either holds or it does not. Faith is always in something, although what it is in may of course prove unreliable.
Beyond this, we don’t know very much about faith, about that which lies at the root of our salvation. The ways we use the word in conversation, what we ‘mean’ by it, the way it functions…all these are matters of curiosity, but not of salvation.
But although we don’t know very much about it, what we do know is important, particularly that it involves willful activity, component A. It is a doing, not a being or an abstraction. It is not the game of baseball, it is a game of baseball. We do not demonstrate faith any more than the players are demonstrating a game. Their playing is the game.
When Jesus lauded the faith of the Syro-Phoenecian woman, he was focused on her activity, because it is the activity that advances the person along the way of salvation. When he called it great, he meant it was impressive, like a brilliant double-play. And when he rewarded her activity, he assured us that such activity is always an advancement, whatever the worldly response.