Given $f(x) = (x - 3)^2 + 4$ and $g ( x ) = \frac { 1 } { x - 4 } - 2$, find and simplify the following:

1. $h(x)= f(x + 2) - 5$

   Hint (a):

   $h(x) = f(x + 2) = 5$
   $h(x) = [((x + 2) − 3)^ 2] + 4 − 5$
   Simplify.

2. $k(x) = g(3 - x) + 2$

   Hint (b):

   $(3 - x)$, the horizontal shift, will replace '$x$' in the $g(x)$ function.
   $+2$, the vertical shift, will be added to the entire '$g(x)$' function.

3. Using set notation, find the domain and range for $g(x)$ and $k(x)$.

   Hint (c):

   Consider the parent graphs of $f$ and $g$.
   Domain and range will shift from that of the parent.
   The parent graph of $f(x)$ is $y = x^2$.
   What is the parent graph of $g(x)$?

   More Help (c):