Question

Select all the transformations undergone from f(x) = x2
to g(x)= −(2x−2)2+2

(4 points)
Responses

reflected across the y-axis
reflected across the y-axis

reflected across the x-axis
reflected across the x-axis

reflected about the origin
reflected about the origin

compressed horizontally
compressed horizontally

stretched horizontally
stretched horizontally

translated to the right
translated to the right

translated to the left
translated to the left

translated up
translated up

translated down

Answer 1

To determine the transformations from the function \( f(x) = x^2 \) to \( g(x) = -(2x - 2)^2 + 2 \), we can break down the process step-by-step:

1. **Start with \( f(x) = x^2 \)**.
2. **Horizontal Compression**: The term \( 2x \) indicates a horizontal compression by a factor of \( 1/2 \) (since \( \frac{1}{2} \) is the reciprocal of 2). Hence, we compress horizontally.
3. **Translation to the Right**: The term \( -2 \) within \( 2x - 2 \) indicates we are translating the graph to the right by 1 unit (the expression \( 2x - 2 \) can be rewritten to show this).
4. **Reflection Across the x-axis**: The negative sign in front of the squared term indicates that we reflect the graph across the x-axis.
5. **Translation Up**: Finally, the \( +2 \) outside the squared term indicates a vertical translation upward by 2 units.

Now, summarizing the transformations:

- Compressed horizontally
- Translated to the right
- Reflected across the x-axis
- Translated up

So, the correct responses are:

- **compressed horizontally**
- **translated to the right**
- **reflected across the x-axis**
- **translated up**