1. The problem statement, all variables and given/known data Give an expression for a function f which has all the following characteristics: f (0) = 4 , and f is increasing for x < 0 , and decreasing for x > 0 , and y = 1 is a horizontal asymptote of the graph of f as x→-∞ , and y = 0 is a horizontal asymptote of the graph of f as x→∞ . 2. Relevant equations Any I guess 3. The attempt at a solution Ok, since part a was to do with trigonometry I figured this being part b might follow suit but after having tried 4cos(x), 4/cos(x) and several other differing equations revolving around some manipulation of cos(0)=1 I've come up totally empty. So then I tried all manner of sorts of x+4 and 1/x +4 but still nothing. I'm not even sure of where to exactly start or how to approach this question aside from trial and error. I can find several equations to fit each characteristic but combining them is stumping me. The only other thing I can think of is a piece wise equation but again I'm not sure how to approach it or where to start. Tips and hints on where to begin are all I'm after, as long as I know I'm on the right path.