Which of the following best describes the transformation that occurs when changing an equation from f(x)=x2+1

Question

to f(x)=(x−3)2+1
?(1 point)
Responses

The graphed function would shift 3 units to the right but otherwise have the same shape.
The graphed function would shift 3 units to the right but otherwise have the same shape.

The graphed function would shift 3 units to the left and would be half as wide.
The graphed function would shift 3 units to the left and would be half as wide.

The graphed function would shift 3 units to the right and would be half as wide.
The graphed function would shift 3 units to the right and would be half as wide.

The graphed function would shift 3 units to the left but otherwise have the same shape.

Answer 1

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.