SOLUTION: I am trying to find the vertical asympote, the horizontal asympote and the x intercept for this problem: {{{y= 6/ (x^2 +4)}}} Then I have to graph it. Can somebody please help me?

To find vertical asymptotes, after simplifying,
set the denominator = 0. 

 +  = 

 = 

 = ±

 = ±

This is imaginary so there are no vertical asymptotes.

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

To find horizontal asymptotes, look at the term on top
and bottom with the largest exponent of x:

1. If the largest exponent on top is greater that the largest
exponent on the bottom, there is no horizontal asymptote.

2. If the largest exponent on top is equal to the largest
exponent on the bottom, the horizontal asymptote has the
equation:

     coefficient of largest power of x on top
y = ------------------------------------------
     coefficient of same power of x on bottom     

3. If the largest exponent on top is less that the largest
exponent on the bottom, the horizontal asymptote is the
x-axis, whose equation is y = 0 

In your peoblem the largest power of x on the top is
the zero power, and the largest poower of x on the bottom
is 2.  So this is case 3, and the horizontal
asymptote is y = 0 or the x-axis.

To graph, find some points:

(-4,0.3), (-2,.75), (0, 1.5), (2,.75), (4,0.3)



There is no x-intercept for the curve never touches
the x-axis but has it as its horizontal asymptote.

Edwin