Consider the function [math].

The x-intercepts occur at [math]
NOTE: If there are more than one, separate your answers by a comma.

There a y-intercept at [math]

To analyze the shape of the graph of [math] it helps to separate the domain into disjoint open intervals [math] whose endpoints [math] are critical points of [math] or [math]. Inside each interval there are no critical points of [math] or [math], so [math] and [math] cannot change sign inside the interval.

[math]
[math]
[math]
[math]
[math]

For each of the intervals listed below, select the curve best representing the shape of the graph of [math] on that interval.

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

 
1   2
 
3   4

(Click on a graph to enlarge it.)