From past experience there is a vertical asymptote at x = 3. This asymptote line should be placed on the graph. Now use the language of limits to describe the function in the vicinity of x = 3.

                                       As x→3+,  y→+¥  As x→3−,  y→−¥

There is an additional complication as x becomes large, either positive or negative. For large x the function becomes large number over large number. If, however, the fraction is multiplied by 1/x over 1/x the limit can be calculated easily as:

This limit produces a horizontal asymptote. This asymptote line should be placed on the graph.  Now how does the curve approach this horizontal line.  When x is greater than 3, the function is positive, and when x approaches 3 from the positive side the function becomes very large, remaining positive. As x approaches 3 from the negative side the function is a large negative number. When x = −2, the function is zero and for numbers less than −2 The function is positive and approaches the horizontal asymptote from below.