Question 147742
First of all, look at the denominator. It factors as (x-4)(x+3).
So, we know that x=4 and x=-3 cannot possibly be valued because they result in division by zero. They are vertical asymptotes. Horizontal asymptote exists at y=1/1     due to the coefficient of the highest degree of the numerator divided by its counterpart in the denominator (squared terms).


Now, f(0)=0/-12=0 is the y-intercept.
f(x)=0 is the x-intercept.

This is, for the most part, all the information you need to produce the following graph (note that you may want to compute values to determine magnitudes of curves for a more accurate graph):
{{{graph( 300, 200, -5, 5, -5, 5, x^2/(x^2-x-12) )}}}

Note that the vertical lines that this site draws in do not belong in the picture.