Question

Select all of the transformations that have been applied to the parent function f(x) = x² to get g(x) = -1/2(x+2)²+3.

Answer 1

To obtain the function g(x) = -1/2(x+2)²+3 from the parent function f(x) = x², the following transformations have been applied: a horizontal translation to the left by 2 units, a vertical compression by a factor of 1/2, and a vertical translation upwards by 3 units.

Step-by-step explanation:

To obtain the function g(x) from the parent function f(x) = x², the following transformations have been applied:

1. Horizontal translation to the left by 2 units: (x + 2)
2. Vertical compression by a factor of 1/2: -1/2(x + 2)²
3. Vertical translation upwards by 3 units: -1/2(x + 2)² + 3