Calculus AB and Calculus BC
CHAPTER 2 Limits and Continuity
The line y = b is a horizontal asymptote of the graph of y = f (x) if
The graph of (Figure N2–4) has the x-axis (y = 0) as the horizontal asymptote.
So does the graph of (Figure N2–5).
The graph of has the line y = 1 as the horizontal asymptote, as shown at the right.
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.
From the graph of in Figure N2–7, describe the asymptotes of k using limits.
SOLUTION: We see that y = 2 is a horizontal asymptote, since
Also, x = 3 is a vertical asymptote; the graph shows that