Consider the functions $f(x) =\text{log}(3 − x)$ and $g ( x ) = \sqrt { x - 3 } - 2$. 

1. What is the domain of each function?

   Hint (a):

   Recall that domains of the parent functions:
   The domain will shift with the function.

2. Graph $h ( x ) = \left\{ \begin{array} { l l } { \operatorname { log } ( 3 - x ) } & { \text { for } x < 3 } \\ { \sqrt { x - 3 } - 2 } & { \text { for } x \geq 3 } \end{array} \right.$ on your graphing calculator.

3. Explain why $h(x)$ is not continuous at $x = 3$?

   Hint (c):

   Consider: $x → 3^−$, $y →$ _________ and $x → 3^+$, $y →$ ________
   Do the left and the right approach the same value?

4. What is the range of each function?

   Hint (d):

   Consider the range of each piece of the piecewise function separately.