The correct response is:
The graphed function would shift 3 units to the right but otherwise have the same shape.
This is because changing \( f(x) = x^2 + 1 \) to \( f(x) = (x - 3)^2 + 1 \) represents a horizontal shift of 3 units to the right, while the shape of the parabola (which remains the same) does not change.