For $f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x - 3 }$ and $g(x) = -x + 2$, find and simplify $h(x) = f(g (x))$

1. Graph $h(x)$ and write its domain in set notation.

   Graph (a):

   

   Answer (a):

   $D = x$ : $x ≠ -1$

2. Find $b(x)$, the end behavior function of $h(x)$.

   Hint (b):

   The end behavior of $h(x)$ will describe what $h(x)$ looks like in the end (as $x→∞$ and as $x→−∞$). Holes and vertical asymptotes are ignored. Observe the graph in part (a). Notice that the graph of $h(x)$ is almost linear. What is the equation of this line? That line, by the way, is $b(x)$, the end behavior of $h(x)$.