1. To find vertical asymptotes, set the denominator equal to zero, or:
(6x2)(3x6) = 0
Now, we can solve for x,
remember if ab = 0, then either a=0 or b=0.
6x2 = 0; x=1/3
3x6 = 0; x=2
2. To find horizontal asymptotes, we compare leading terms. We know that the top and bottom are both polynomials with degree 2. Let's multiply them out to
(6x^{2} + ...)/(18x^{2}  ...)
As x gets very large in either direction , f(x) tends towards the "a" term in these quadratics. Therefore, the horizontal asymptote is
y = 6/(18); y=1/3
Likewise, as x gets very small, f(x) tends towards the "c" term in these quadratics. Therefore, the other horizontal asymptote is
y=18/12; y=3/2
3. To find xintercepts we set f(x) = 0 and solve for x. The first step is to find the numerator = 0, because
0/anything = 0
0 = (6x6)(x+3)
another quadratic
6x6 = 0 x=1
3x6 = 0 x=2
4. To find the yintercepts, we set x=0 and solve for f(x)
(6(0)6)(0+3)/(6x2)(3(06))
=(6)(3)/((2)(6))
f(x) = 3/2
y= 3/2
2/9/2014

Benjamin M.