1. Determine the intercepts, if there are any.  Recall that the y-intercept is specified by

(0, f (0)) and we determine the x-intercepts by setting the numerator equivalent to zero and solving.

2. Determine the vertical asymptotes by setting the denominator equivalent to zero and solving.

3. Determine the horizontal asymptote, if it present, using the fact above.

4. The vertical asymptotes will divide the number line in different regions. In each of region graph at least one instance in each of region. This point will tell us whether the graph will be above or below horizontal asymptote and if we have to we must get various points to determine the general shape of the graph.

5. Sketch the graph.

Note that the sketch that we'll get from the procedure is going to be a pretty rough sketch however that is okay.  That's all that we're actually after is a basic idea of what the graph will look at.