Let's analyze each transformation one by one:
1. Vertical stretch or compression:
- The coefficient before \( f(x) \) is -2. Since it's negative, it reflects the graph over the x-axis and compresses it vertically by a factor of 2.
- So, the box "vertical stretch or compression" is checked.
2. Reflection over the x-axis:
- As mentioned earlier, the coefficient before \( f(x) \) is negative, indicating a reflection over the x-axis.
- So, the box "reflection over the x-axis" is checked.
3. Horizontal translation:
- The expression \( f(x - 13) \) indicates a horizontal translation of 13 units to the right.
- So, the box "horizontal translation" is checked.
4. Vertical translation:
- The constant term -35 indicates a vertical translation of 35 units downwards.
- So, the box "vertical translation" is checked.
Therefore, the checked boxes are:
- [x] Vertical stretch or compression
- [x] Reflection over the x-axis
- [x] Horizontal translation
- [x] Vertical translation
