To obtain a new graph, stretch the graph of a function $f(x)$ vertically by a factor of 3. Then shift the new graph 6 units to the right and 3 units up. The result is the graph of a function $$g(x) = A f(x+B) +C$$ where $A$, $B$, $C$ are certain numbers. What are $A$, $B$, and $C$?

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