Find the verticle asymptote of the rational 
function  
Possible answers: 
y = 1/2
y = 3/4
y = 2
y = 4 
Thank you. Exactly what is a asymptote? Can anyone 
explain the simplest way to solve this problem?

-------------------------------------------------

Something is wrong!  Asymptotes are straight 
lines.  All those choices are equations of 
HORIZONTAL lines, not of VERTICAL lines.  
Yet you asked for the VERTICAL asymptote.  The 
vertical asymptote has equation  and the 
HORIZONTAL asymptote has equation .  
Did you copy something wrong?  Did you type y's 
where there should be x's, or did you type "verticle" 
(sic) when you meant "horizontal"?

First I'll have to show you how to solve the 
problem by graphing. Then I'll show you the simplest 
way.  But you must understand what an asymptote
is before you can know what you are doing.

Let's graph 
Get some points:

  x  f(x)
-10  1
-7   1.1
-3   1.5
-2   1.8
0    6
2    -1
4    0
8   .4
11  .5 



The graph of the function is in green.  But 
I have drawn two extra lines in, a blue vertical 
line and a red horizontal line. These lines are
called "asymptotes". Look at the blue vertical 
line that goes through 1/2 on the x-axis? The 
green curve approaches that green line but never 
touches it. That line is called the vertical 
ASYMPTOTE.  I also drew in the horizontal 
asymptote in red.

As you can see, that green vertical asymptote has 
the equation . and that blue 
horizontal asymptote has the equation .

Now here is the easy way to find the equation of that blue 
vertical asymptote without having to graph:

Set the denominator of  equal
to zero, because a function is undefined if x has a value
which causes the function to be undefined.  You know
that having a 0 in the denominator causes a fraction to be
undefined, right?  So we have


  
   

That's all there is to finding the equation of the vertical 
asymptote.

Now to find the horizontal asymptote, the red line. 
Since numerator and denominator have the same degree 
(same largest exponent of x), we merely get the 
quotient of the coefficients of the largest powers 
of x.  The coefficient of x in the numerator is 3 
and the coefficient of x in the denominator is
4, so we make the fraction and write
 as the equation of the red horizontal 
asymptote.

Edwin