Consider the function [math].

The y-intercept is at: [math]
There a horizontal (or oblique) asymptote at [math]
NOTE: This could be a function of x.

If [math], [math], and [math] are critical points, then [math] can be broken up into the following unique intervals:
([math]), ([math]), ([math]), ([math]).

[math]
[math]
[math]

For each of the intervals listed below, select the graph best representing the shape of the function in that interval.

([math]):
      ([math]):
      ([math]):
      ([math]):

 
1   2
 
3   4

(Click on a graph to enlarge it.)