I am trying to come up with a function y=f(a) that includes a fixed parameter b such that the graph has a minimum at x=0, a maximum of 1 at x=b, and a right tail that approaches the x-axis asymptotically as x approaches infinity after x>b. I want the function to approximate the combinationof y=x/b where x<s, and y=b/x where x>b, but with a smooth curve. Any insight would be greatly appreciated. Thanks!