Find all vertical asymptotes and/or holes of the function
First we factor:
The denominator has two roots: x = -4 and x = -2. Each of these will provide us with either a hole or a vertical asymptote.
When we simplify f, we find
Since the root x = -2 is left over after simplification, we have a vertical asymptote at x = -2.
Since the root x = -4 canceled out during simplification, the function will have a hole when x = -4. The y-value of the hole is
Now we know a little bit about what the function will look like:
PICTURE: hole at (-4,4) and vertical asymptote (dashed line) at x = -2.