Question: Given X ~ U(0,3) and function

\[g\left( x \right)=\left\{ \begin{aligned} & x\,\,\,\,\,\,\,0\le x\le 2 \\ & 2\,\,\,\,\,\,\,2\le x\le 3 \\ & 0\text{ elsewhere} \\ \end{aligned} \right.\]

find the CDF of Y = g(X). Is X continuous? As a function of X, is Y continuous or discrete?