The line x = a is a vertical asymptote of the graph of y = f (x) if one or more of

the following holds:

The graph of (Figure N2–4) has x = 0 (the y-axis) as the vertical

asymptote.

The graph of (Figure N2–5) has x = 1 as the vertical asymptote.

The graph of (Figure N2–6) has the line x = 2 as the vertical

asymptote.

###### Example 8 **__**

**__**From the graph of in Figure N2–7, describe the asymptotes of k

using limits.

`Figure N2–7`

SOLUTION: We see that y = 2 is a horizontal asymptote, since

Also, x = 3 is a vertical asymptote; the graph shows that