I've been having issues seeing functions that have denominators. I have few issues understanding most regular functions and how they are manipulated but in my effort to return to school I have missed out on understanding functions when combined with a denominator.

For example: $\displaystyle f(x)=\frac{|x-1|}{2-2x}$

Is there any method to seeing that the lines are at +1/2 and -1/2? Is there a good website that can teach me methods of visualizing various fraction functions?