Question

Let f(x) = x² - 3. Let g(x) = (x + 2)² - 5. Select all statements below that describe the transformation of f(x) to g(x).

Answer 1

The function g(x) is obtained from f(x) by the following sequence of transformations:

1. A horizontal shift left by 2 units (x + 2).
2. A vertical shift down by 5 units (-5).
3. A vertical stretch by a factor of 1 (the squared term does not change the stretch factor).
4. A reflection about the x-axis (the negative sign in front of the 5).

Therefore, the correct statements are:

- A horizontal shift left by 2 units.
- A vertical shift down by 5 units.
- A reflection about the x-axis.

Answer 2

The vertex of g(x) is translated left by 2 units and down by 5 units compared to the vertex of f(x).

The shape of the parabola for g(x) is the same as the shape of the parabola for f(x).

The axis of symmetry for g(x) is the same as the axis of symmetry for f(x).

The minimum point of g(x) is lower than the minimum point of f(x).