The graph of f(x) = 2x must be shifted seven units to the right to produce the graph of g(x) = 2^(x - 7).
To shift the initial graph of f(x) = 2x, we replace the x with (x - 7). This shifts the digits to the right, as 7 indicates how much we shift the graph by.
Ultimately, the graph must be shifted a total of 7 units to the right.