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

1. is decreasing
2. is concave up

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

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


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

C. What happens to as ?

(Enter the value, 'infinity' or '-infinity' for or , or 'none' if there is no limit.)

You can earn partial credit on this problem.