Well, the thread here: http://www.mathhelpforum.com/math-he...tml#post144408
Originally Posted by mikedwd
goes a long way to solving the problem.
But doing it your way, you have
but you get the wrong value of y for the hole. You get (2, -4) instead of (2, -2) .....
2x(x-2) / (x-3)(x-2)
Anyway, persevering with your way:
The problem with your function is that you need to be modified in some way so that when x = 2, y = -2. At the same time you need to make sure that y = 2 remains a horizontal asymptote .......
So why not consider finding the value of A such that
gives y = -2 when x = 2 ......
y = (2x + A) / (x-3)
Then your final function will be
which can be simplified as necessary.
(2x + A)(x-2) / (x-3)(x-2)
You will get the answer I found at the above hyperlink.