To determine the domain of the position of a video game character based on the given piecewise function, we typically need to know the constraints that define the values of \( x \) (horizontal position) and \( y \) (vertical distance from the bottom of the screen). Unfortunately, the piecewise function itself is not provided in your message, but we can infer from the choices presented.
When considering the possible intervals:
- [5, 8]: This would mean that the character can only be positioned horizontally between 5 cm and 8 cm.
- [-2, 8]: This includes the possibility of negative horizontal positions which might not be valid depending on the context (screen positions usually can't be negative).
- [4, 8]: This means horizontal positions starting from 4 cm to 8 cm.
- [0, 8]: This allows for horizontal positions starting from the left edge of the screen at 0 cm to 8 cm.
From a logical perspective, if we consider only valid horizontal positions and if the character cannot be positioned before 0 cm, the most appropriate interval would be [0, 8].
Thus, based on this reasoning, unless negative positions are permissible according to the specific definition in your piecewise function:
The domain of \( x \) in interval notation is most likely [0, 8].