### Home > PC3 > Chapter 11 > Lesson 11.2.3 > Problem11-117

11-117.

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

1. Sketch $y = h(x)$.

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

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

Are there any inputs for $g$ that will produce an undefined output?

1. What is the domain of $h(x)$?

$x ≠ ?$

1. What is $\lim\limits _ { x \rightarrow - \infty } h ( x )$?

Review the graph of $y = h(x)$. What is the horizontal asymptote?