We want to find $h ( x ) = \frac { 1 } { g ( x ) }$ where $g ( x ) = \left\{ \begin{array} { l l } { 2 x + 2 } & { \text { for } x < 1 } \\ { 3 - x } & { \text { for } x > 1 } \end{array} \right.$.

1. Sketch $h\left(x\right)$.

   Graph g(x):

   

   Graph h(x):

   

2. What is the domain of $g\left(x\right)$?

   Answer (b):

   $\left(−∞, 1\right) ∪ \left(1, ∞\right)$

3. What is the domain of $h\left(x\right)$?

   Answer (c):

   $x ≠ −1, 1, 3$

4. What is $\lim\limits_ { x \rightarrow - \infty } h ( x )$?

   Answer (d):

   $0$