CPM Homework Help : PC3 Problem 11-117

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

Sketch $y = h(x)$ .
Hint (a):
Start by sketching $y = g(x)$ . The $x$ -intercepts will be the vertical asymptotes of the reciprocal function.

What is the domain of $g\left(x\right)$ ?
Hint (b):
Are there any inputs for $g$ that will produce an undefined output?

What is the domain of $h(x)$ ?
Hint (c):
$x ≠ ?$

What is $\lim\limits _ { x \rightarrow - \infty } h ( x )$ ?
Hint (d):
Review the graph of $y = h(x)$ . What is the horizontal asymptote?