From the problem :

, in this case the function is decreasing.

, in this case the function is increasing.

.

Let us consider a function which satisfy t .

The first derivative is .

The second .

Draw the coordinate plane.

Graph the function .

Graph :

Observe the graph :

The graph has no inflection points and has horizantal asymptotes at .

Yes, it is possible to sketch a graph of a function that satisfies the conditions as it has no points of inflection.