1. In symbol, we write this as
LIMIT AT INFINITY
Consider the function
Investigate the behavior of f(x) as x decreases
without bound x -1 -5
-10
-100
-1000
-10,000
f(x) 1
1.92
1.98
1.9998
In symbol, we write this as

2. In symbol, we write this as
Consider the function
Investigate the behavior of f(x) as x increases
without bound x 1 5 10
100
1000
10,000
f(x)
1.92
1.98
1.9998
In symbol, we write this as

3. horizontal asymptote

4. Theorem : Let n be a positive integer, then

8. Horizontal asymptote

9. x = -2 (vertical asymptote) y = 2 is a horizontal asymptote
Dh: all x R except x = -2
When x = 0 , y = - 3 (y – int)
When y = 0 , x = 3 (x – int)
x = -2 (vertical asymptote)
y = 2 is a horizontal asymptote x
- 4
- 3
- 1
y = h(x) 7 12
- 8 9

10. x = -2 (vertical asymptote) y = 2 is a horizontal asymptote
Dh: all x R except x = -2
horizontal asymptote
y = 2
x = -2 (vertical asymptote) x
- 4
- 3
- 1
y = h(x) 7 12
- 8
(0, -3) , (3, 0)
vertical asymptote
x = -2
y = 2 is a horizontal asymptote 10

11. Df: all x R except x = -2 & x = 2
When x = 0 , (y – int)
When y = 0 , x = -1 (x – int)
x = -2 (vertical asymptote)
x = 2 (vertical asymptote) x -4 -3
-1.5 1 3 4
f(x)
(-1/4)
(-2/5)
(2/7)
(-2/3)
(4/5)
(5/12)
-0.25
-0.4
0.286
-0.67
0.8
0.417
y = 0
(horizontal asymptote) 11

12. Df: all x R except x = -2 & x = 2
x = -2 (vertical asymptote)
vertical asymptote
horizontal asymptote
x = -2
y = 0
x = 2 (vertical asymptote)
x = 2
vertical asymptote
y = 0 (horizontal asymptote) x -4 -3
-1.5 1 3 4
f(x)
(-1/4)
(-2/5)
(2/7)
(-2/3)
(4/5)
(5/12)
-0.25
-0.4
0.286
-0.67
0.8
0.417 12