Fortunately the function has been factorised for us, so we can see what values of x in and outside the bracketed factors are needed to make those factors zero. That's a good start for answering the question, which appears to be a long-standing one. The values of x that produce zero factors are: 0, -2, 1, 4 and -3. These, as we'll see, have different meanings, depending on where they are in the function. The factors in the numerator simply make the function zero; but those in the denominator give rise to vertical asymptotes. The vertical asymptotes are therefore the lines x=4 and x=-3. The other three values of x represent intercepts: y=f(x)=0 when x=0, -2 and 1. So the x intercepts are (0,0), (-2,0) and (1,0). When x=0, f(x)=0, so the origin (0,0) is both an x and a y intercept. There are no others. There is another asymptote which is neither horizontal nor vertical. When x is very, very, large, the numbers become insignificantly small by comparison, and the function becomes 3x^3/x^2=3x. The line y=3x is therefore an asymptote. This is a line with positive slope 3 passing through the origin. The graph, which is in three parts, never quite touches this line. The central portion sits between the two vertical asymptotes, while the other two sections are outside the asymptotes and these sections are the ones to which the asymptote y=3x applies as well as the vertical asymptotes.