A continuous function [math], defined for all [math], has the following properties:

1. [math] is decreasing
2. [math] is concave up
3. [math]
4. [math]

Sketch a possible graph for [math], and use it to answer the following questions about [math].

A. For each of the following intervals, what is the minimum and maximum number of zeros [math] could have in the interval? (Note that if there must be exactly N zeros in an interval, the minimum and maximum are both N.)

minimummaximum
[math]
[math]
[math]
[math]

B. Are any of the following possible values for [math]? (Enter your answer as a comma-separated list, or enter 'none' if none of them are possible.) [math], [math], [math], [math], [math], [math], [math], [math], [math].
possible values: [math]

C. What happens to [math] as [math]?
[math]
(Enter the value, 'infinity' or '-infinity' for [math] or [math], or 'none' if there is no limit.)