Let $f(x) = \left\{ \begin{array} { c c c } { 2 - x ^ { 2 } } & { \text { for } } & { x \leq 1 } \\ { x } & { \text { for } } & { x > 1 } \end{array} \right.$. 

1. Let $g(x) = f(x) + 2$. Sketch the graphs of $y = f(x)$ and $y = g(x)$ on the same axes.

   Hint (a):

   Shift the original function up $2$ units.

2. Write an equation for $g(x)$.

   Hint:

   Since the function is shifted up, there is no change in the domain.
   The first part of the function becomes $2-x^2+2$.