Assume that \(f: (-2, -1) \to (1, 2)\) is an onto function and for \(i = 1, 2, 3, 4\), define \(g_1(x) = f(x) - 2\), \(g_2(x) = f(-x)\), \(g_3(x) = -f(-x)\) and \(g_4(x) = f(-x - 2)\). What is the correct arrangement of \(g_1, g_2, g_3, g_4\) such that the graph of the \(k^{\text{th}}\) function lies in the \(k^{\text{th}}\) quadrant for \(k = 1, 2, 3, 4\)?