How does the graph change from f(x)f(x) to g(x)g(x) ?
g(x) = 2x - 3 + 2 = 2x - 6 + 3 + 3 - 1 = (2(x + 3) - 6 + 3) - 1 = f(x + 3) - 1
So
the graph of g(x) is the graph of f(x) shifted 3 units left and 1 unit down.
