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. |