The correct response is:
The graphed function would shift 3 units to the right but otherwise have the same shape.
To elaborate, when transforming the function from \( f(x) = x^2 + 1 \) to \( f(x) = (x - 3)^2 + 1 \), the \( (x - 3) \) indicates a horizontal shift to the right by 3 units, while the shape of the graph remains the same since there is no change in the coefficient in front of \( x^2 \) that would affect the width. The "+1" adjusts the vertical position but does not affect the horizontal shift.