Select all the transformations undergone from f(x) = x2

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