Executing Limit within a Function

Question

I am trying to create a Mathematica function where f[0] = 0, f[1] = 1 and f[10] = $\infty$, ala Warp Speed from Star Trek. When I designate the following function:

f[x_] = Limit[90 / (10 - a) - 9, a -> x, Direction -> 1];

I get $f[x]=\frac{9 x}{x - 10}$ and $f[10] = ComplexInfinity$, where it executes the limit before it adds in the variable. How do I make it go the other way around, where the limit waits for the variable to come in first. Is that possible?