Sketch a continuous curve which meets all the criteria:
for all is concave down.
How many roots do
Is it possible for a function that is always increasing (hint 1) AND always concave down (hint 2) to have no roots?
What can you say about the location of the root(s)?
On what domain could the root(s) not exist?
Could there be a horizontal asymptote as
Is it possible that
? ? For each case, explain why or why not.