How can I mathematically represent a graph like this?s

Question

I apologize for the HORRIBLE graphic, but what is the equation of a line like the one above? The gradient increases the closer x gets to 1

Answer 1

It could be something like

$$f(x)=\frac x{1-x}\;,\;\;0\le x<1$$

Answer 2

Another function: $$f(x)=\tan\left(\frac{\pi x}{2}\right)\;,\;\;0\le x<1$$ whose graph can be seen HERE .