x - intercepts: To find the x-intercept(s), replace y with 0 (zero) and solve for x
y-intercepts: To find the y-intercepts, replace x with 0 (zero) and solve for y
Vertical: To find the vertical asymptotes for a rational function, we find the x's that make the denominator zero. so x = (whatever) is the vertical asymptote if when x is that value, the denominator becomes zero. (there may be more than 1 such value)
Horizontal: To find horizontal asymptotes for a function f(x), find and . if either of those limits give you a finite value, that is your horizontal asymptote. we equate y to whatever finite value we get and call that the vertical asymptote, so for instance, if we find that , we say is a vertical asymptote.
Oblique/Slant: If there are no horizontal and/or vertical asymptotes, or just for good measure because it is required on your exam, it is good to check for slant asymptotes. To find these, perform the division indicated. that is, use polynomial long division (or synthetic division if you prefer) to actually divide the numerator by the denominator. The quotient of this division is the line for the slant asymptote.
It is hard to describe how to draw the graph in words (i would try, but i don't have time now), and i fear i cannot give you any more information than this, since you are doing a test, it would be helping you to cheat. So my suggestion is, search the forum for similar problems, they are all around, and use them to help you. (Click on the "search" button in the menu bar, a drop down menu will appear with a slot to enter your search phrase)