College Algebra 9th txtbk

SECTION 4–4 Rational Functions and Inequalities 313
9. y
10.
10
10
y
27. p(x) x2 2x 1
28.
x
q(x) x3 1
x 1
10
10
x
10
10
x
29. h(x) 3x2 8
30.
2x 2 6x
k(x) 6x2 5x 1
7x 2 28x
In Problems 31–34, explain why each graph is not the graph of a
rational function.
10
31.
y
11. Let f (x) 2x 4 Complete each statement:
x 2 .
(A) As x S 2 , f (x) S ?
(B) As x S 2 , f (x) S ?
(C) As x S , f (x) S ?
(D) As x S , f (x) S ?
5
5
5
x
12. Let g(x) 2x 4 Complete each statement:
2 x .
(A) As x S 2 , g(x) S ?
(B) As x S 2 , g(x) S ?
(C) As x S , g(x) S ?
(D) As x S , g(x) S ?
32.
5
y
5
13. Let h(x) 2x 4 Complete each statement:
x 2 .
(A) As x S 2 , h(x) S ?
(B) As x S 2 , h(x) S ?
(C) As x S , h(x) S ?
(D) As x S , h(x) S ?
14. Let k(x) 4 2x Complete each statement:
x 2 .
(A) As x S 2 , k(x) S ?
(B) As x S 2 , k(x) S ?
(C) As x S , k(x) S ?
(D) As x S , k(x) S ?
33.
5
3
5
y
3
3
5
x
x
In Problems 15–22, find the domain and x intercepts.
3
15. f (x) 3x 9
x
16. g(x)
17. h(x) x 6
x 2 4
18.
2x 10
x 1
k(x) x2 9
x
34.
y
5
19. r(x) x2 3x 4
20.
x 2 1
s(x) x2 4x 5
x 2 4
5
5
x
21. F(x) x4 16
22.
x 2 36
G(x) x4 x 2 1
x 2 25
5
In Problems 23–30, find all vertical and horizontal asymptotes.
23. f (x) 5x 1
24. g(x) 7x 2
x 2
x 3
25. s(x) 2x 3
26. t(x) 3x 4
x 2 16
x 2 49
In Problems 35–38, explain how the graph of f differs from the
graph of g.
35.
f (x) x2 2x
; g(x) x 2
x
36. f (x) x 5
x 2 25 ; g(x) 1
x 5