Let $u_{g}(x)$ Be Julie's Utility Function Over Gains And $u_{l}(x)$ Her Utility Function Over Losses

Multiple Choice

Let $u_{g}(x)$ be Julie's utility function over gains and $u_{l}(x)$ her utility function over losses. If Julie's preferences are best described with Prospect Theory, which of the following is an example of Julie's value function?

A) $\quad v(x \mid 0) = \begin{cases}\ln (x) , & x>0 \\ 0, & x=0 \\ -x, & x<0\end{cases}$
B) $\quad v(x \mid 0) = \begin{cases}\mathrm{X}, & x>0 \\ 0, & x=0 \\ -\ln (-x) , & x<0\end{cases}$
C) $\quad v(x \mid 0) =\left\{\begin{array}{l}x, x>0 \\ x, x=0 \\ x, x<0\end{array}\right.$
D) $\quad(x \mid 0) =\left\{\begin{array}{c}\ln (x) , x>0 \\ -\left(x^{2}\right) , \quad x \leq 0\end{array}\right.$