For (1), you need a "solid dot" at (0,2) and an "open circle" at (0,0). Similarly, you need a "solid dot" at (4,1) and "open circles" at (4,0) and (4,3).
In problem (2) you factored to get , which is incorrect. You only need to factor the denominator to get . The answer is still .
For (3), has two zeros, which will be vertical asymptotes of the function. As x goes to or , y goes to . Beyond that, I think you might have to calculate a few points. A graphing calculator or graphing tool on the computer is good for checking your work.