1. rational functions

okay i am given paramaters and need to make a rational function with them. I'm having a hard time coming up with the right function.

1. HA: y=2
VA: x=-2
a single zero at 4, and y-int (0, -4)

2. HA: y=0
VA: x=-6, x=3
a zero at -3, y int (0, .5

2. First Problem

The answer to 1 is:

$f(x)=\displaystyle\frac{-12}{x+2}+2$

To get this, first I found what graph made the asymptotes work. Remember that adding a value on the end (such at the +2) will raise the asymptote while adding a value to x will shift it left and right. Then I messed with the numerator until I got it right.

3. Also how is one supposed to make a function with a horizontal asymptote at y=0 and yet have a point that makes it equal to 0. I am rather confused.