Plotting Points
When all  else fails!

Check out the rational function Grapher/Tutorial at joemath.com

Let's graph 

Start by making a table of values....

x y
-3 -1/5 = -.2
-2 -1/4 = -.25
-1

-1/3 »-.3

0 -1/2 = -.5
1

 -1/1 = -1

2

undefined

3  1/1 = 1
4 1/2 = .5
5 1/3 ».3
6 1/4 = .25

Plot these points

Try to be accurate
Plot (-3, -.2) , (-2, -.25)

(-1, -.3) .....

Find more points

What happens at near 2?
Plug in values close to 2 like 2.5, 2.2, 2.1, 2.01
(2.5, 2)
(2.2, 5))
(2.1, 10)
(2.01, 100)

Plot these new points

As we get closer to 2 we see that y gets very large (and small) quickly .
Plug in values close to 2 like 1.5, 1.8, 1.9, 1.99
(1.5, -2)
(1.8, -5)
(1.9, -10)
(1.99, -100)
Plot these new points

As x gets large (or small) y gets closer to zero.
I made this with MathCAD.  Note the vertical asymptote at  x = 2 and the horizontal asymptote at y = 0.

Check out the rational function Grapher/Tutorial at joemath.com