You can see what it looks like by entering this into Google: plot((x^2+2x-8)/(x^2+6x+8))
Make sure you zoom out using the mouse wheel. There are two parts to the graph.
Note:
(x^2 + 2x - 8) / (x^2 + 6x + 8)
(x+4)(x-2) / (x+4)(x+2)
(x-2)/(x+2) with a hole knocked out at x = -4
Since you can't have 0 on the bottom of a fraction, x+2 can't be 0, so x can't be -2.
There's a vertical asymptote at x = -2.