This is a function in the "general" form of . The graph of takes on all values except for , and thus 0 is indeed a vertical asymptote of the function. This makes sense for you as you know that you can not divide a number by 0. However what about the horizontal asymptote? Try to solve for , and see what you get.
Now lets take a look at negative values of x (or s in your problem). With negative values of s, we get a "negative" percentage. However, does that make sense in the CONTEXT of this problem.
I'll give you another example involving context. Lets say the amount of miles I can drive a car is modeled by the function: , where X is the amount of fuel in my car. The graph of is a straight line that takes on ALL real numbers. However lets think about this in the CONTEXT of the problem. Can I put in NEGATIVE values for X? Of course not, I can't drive on negative 10 gallons of gas can I?
The same applies to your problem above. Break down the problem and try to make a sentence out of what the equation is. For my problem it would be:
If I put in negative gallons of fuel, I will drive negative miles!