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

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

Answer 1

The transformation from the equation \( f(x) = x^2 + 1 \) to \( f(x) = (x - 3)^2 + 1 \) involves a horizontal shift.

Specifically:

• The expression \((x - 3)\) indicates a shift to the right by 3 units.
• The "+1" at the end does not affect the horizontal transformation and simply indicates a vertical shift up by 1 unit.

However, the problem only asks about the horizontal transformation.

Therefore, the correct answer is:

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