The image shows a parent function f(x)=x2

Question

𝑓
(
𝑥
)
=
𝑥
2
and a translated form f(x)=x2−3
𝑓
(
𝑥
)
=
𝑥
2
−
3
. Which statement best describes this translation?

(1 point)
Responses

The function shifted vertically down 3 units and is wider than the original.
The function shifted vertically down 3 units and is wider than the original.

The function shifted horizontally to the right 3 units and is narrower than the original.
The function shifted horizontally to the right 3 units and is narrower than the original.

The parent function shifted vertically down 3 units and did not change in any other way.
The parent function shifted vertically down 3 units and did not change in any other way.

The parent function shifted horizontally to the right 3 units and did not change in any other way.

Answer 1

The correct statement is:

The parent function shifted vertically down 3 units and did not change in any other way.

This is because the translation \( f(x) = x^2 - 3 \) indicates that the entire graph of the parent function \( f(x) = x^2 \) has been moved down 3 units without any horizontal shift or change in width.