Even-Numbered Answers to Exercise Set 5.6:
Rational Functions
Math 1300, Fundamentals of Mathematics
The University of Houston Solutions to Chapter 5 Exercises
2. (a) (0) 1f=
(b)
(5)f− is undefined.
(c)
(
)
25
1
26
5
f=
4. (a) 7
6
(0)f=−
(b) 15
2
(4)f=−
(c)
()
22
3
27
4
f−=
6. (a) 5
9
(4)f−=−
(b) (0) 1f=−
(c)
(1) 0f=
8. (a) 1
14
(0)f=−
(b) 1
8
(1)f−=−
(c)
(7)f is undefined.
10. (a) 5
12
(0)f=−
(b) 1
2
(2)f−=−
(c) (5) 0f−=
12. (a) Domain: 2x≠−
(b) Vertical asymptote at 2x=−
(c) x-intercept: 6−
y-intercept: 3
(d) 7
3
(1)f=; (1) 5f−=
(e) Graph III
14. (a) Domain: 2x≠−
(b) Vertical asymptote at 2x=−
(c) x-intercept: 4
y-intercept: 2−
(d) (1) 1f=− ; (1) 5f−=−
(e) Graph I
16. (a) Domain: 0x
≠
(b) Vertical asymptote at 0x=
(c) x-intercept: None
y-intercept: None
(d) (1) 8f
=
−; (1) 8f
−
=
(e) Graph I
18. (a) Domain: 2x
≠
(b) Vertical asymptote at 2x=
(c) x-intercept: None
y-intercept: 4
−
(d) (1) 8f
=
−; 8
3
(1)f
−
=−
(e) Graph IV
20. (a) Domain: 3x
≠
(
)( )
,3 3,
−
∞∞∪
(b) Vertical asymptote: 3x=
(c) x-intercept: None
y-intercept: 4
22. (a) Domain: 8x
≠
(
)( )
,8 8,
−
∞∞∪
(b) Vertical asymptote: 8x=
(c) x-intercept: 0
y-intercept: 0
24. (a) Domain: 1x
≠
−
(
)( )
,1 1,
−
∞− − ∞∪
(b) Vertical asymptote: 1x=−
(c) x-intercept: 4
y-intercept: 4
26. (a) Domain: 4, 4xx
≠
−≠
(
)( )
(
)
,4 4,4 4,
−
∞− − ∞∪∪
(b) Vertical asymptotes: 4, 4xx=− =
(c) x-intercept: 8
y-intercept: 1
2
