To find the vertical asymptote, set the denominator equal
to zero and solve for x:




 is the equation of a vertical line 4 units right of
the y-axis, so we draw that vertical asymptote:



There will be a horizontal asymptote whenever the (degree) largest
exponent of x in the top is not larger than the largest
exponent of x in the bottom.  When the degrees of the top is
smaller, the horizontal asymptote is the line  but
when the degrees are the same the horizontal asymptote is



The coefficient of x on the top is 2, and the coefficient of x
on the bottom is 1, so the horizontal asymptote is  or
. That is a horizontal line 2 units above the x-axis.
Let's draw it:



Now we need to get some points on both sides of all asymptotes:

(-4,1), (0,0), (2,-2), (3,-6), (5,10), (6,6), (8,4)

Plot those points:



Draw a smooth graph through the points:



The vertical asymptote is 
The horizontal asymptote is 

Edwin