1. To find vertical asymptotes, set the denominator equal to zero, or:
(-6x-2)(3x-6) = 0
Now, we can solve for x,
remember if ab = 0, then either a=0 or b=0.
-6x-2 = 0; x=-1/3
3x-6 = 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 x-intercepts we set f(x) = 0 and solve for x. The first step is to find the numerator = 0, because
0/anything = 0
0 = (6x-6)(x+3)
another quadratic
6x-6 = 0 x=1
3x-6 = 0 x=2
4. To find the y-intercepts, we set x=0 and solve for f(x)
(6(0)-6)(0+3)/(-6x-2)(3(0-6))
=(-6)(3)/((-2)(-6))
f(x) = 3/2
y= 3/2