Answer
Sample answer: $\quad h(x)=\left\{\begin{array}{lll}
-1 & for & x\lt 0\\
1 & for & x\geq 0
\end{array}\right.$
Work Step by Step
There are no vertical asymptotes (h does not need to be a rational function.)
On the far left side, the graph can approach $y=-1$,
(it can also be that $h(x)=-1, $ for $x\lt 0)$
On the far right side, the graph can approach $y=1$,
(it can also be that $h(x)=1, $ for $x\gt 0)$
At x=0, h can be undefined, or not. Let our $h(0)=1$.
The function $h(x)=\left\{\begin{array}{lll}
-1 & for & x\lt 0\\
1 & for & x\geq 0
\end{array}\right.$
satisfies the conditions.
