Graphically Determining Limits
For the function y = f (x ) below, y = 0 and x = −4 are asymptotes. Use the graph to find the following
values (if possible):
1.
2.
3.
4.
5.
6.
lim f ( x )
13. lim f ( x )
8.
lim− f ( x )
14. lim+ f ( x )
9.
lim f ( x )
15. lim f ( x )
f (− 2 )
7.
lim f ( x )
x → −2 +
lim f (x )
x → −2
x →1+
x →1
x →1
x →3
x → −4
x →∞
lim f (x )
10. f (3)
16. f (1)
lim f ( x )
11. lim+ f ( x )
17. lim f ( x )
lim f ( x )
12. lim− f ( x )
18. f (− 4 )
x → −1+
x → −1−
x → −1
x →3
x →3
x → −3
Use the graph of y = f ( x ) below, where y = 0 and x = 5 are asymptotes, to find the following values (if
possible):
1.
2.
3.
lim f ( x )
7.
lim f ( x )
13. lim− f ( x )
lim f ( x )
8.
f (5)
14. lim+ f ( x )
lim f ( x )
15. lim f ( x )
x → −3−
x → −3+
lim f ( x )
9.
x → −1−
x → −3
4.
f (− 3)
5.
lim− f ( x )
6.
x →5
x →5
lim f ( x )
x →5+
x →2
x →2
x→2
10. lim+ f ( x )
16. f (2 )
11. lim f ( x )
17. lim f ( x )
12. f (− 1)
18. lim f ( x )
x → −1
x → −1
x →∞
x → −∞