C H A P T E R 2 Polynomial and Rational Functions

224 Chapter 2 Polynomial and Rational Functions
11.
13.
15.
Critical numbers: x 7, x 3
Test intervals: , 7, 7, 3, 3,
Test: Is x 7x 3 < 0?
Interval x-Value Value of
x 7x 3
Conclusion
, 7
7, 3
3,
x 2 4x 4 ≥ 9 14.
x 2 4x 5 ≥ 0
x 5x 1 ≥ 0
Critical numbers: x 5, x 1
Test intervals: , 5, 5, 1, 1,
Test: Is x 5x 1 ≥ 0?
Interval x-Value Value of
x 5x 1
Conclusion
, 5 x 6 17 7 Positive
5, 1 x 0 51 5 Negative
1, x 2 71 7 Positive
Solution set: , 5 1,
−6 −5 −4 −3 −2 −1
0
1
Critical numbers: x 3, x 2
Test intervals: , 3, 3, 2, 2,
Test: Is x 3x 2 < 0?
2
x
Interval x-Value Value of
x 3x 2
Conclusion
, 3
3, 2
2,
x 2 2 < 25
x 2 4x 4 < 25
x 2 4x 21 < 0
x 7x 3 < 0
Solution set:
Solution set:
x 10
x 0
x 5
7, 3
x 2 x < 6 16.
x 2 x 6 < 0
x 3x 2 < 0
x 4
x 0
x 3
3, 2
313 39
73 21
122 24
−7
−8 −6 −4
−2
16 6
32 6
61 6
0 2
−3 −2 −1 0 1 2
3
4
Positive
Negative
Positive
x
Positive
Negative
Positive
x
12.
x 2x 4 ≥ 0
Critical numbers:
Test intervals: , 2 ⇒ x 2x 4 > 0
Solution intervals: , 2 4,
x 1x 7 < 0
Critical numbers:
Test intervals: , 1 ⇒ x 1x 7 > 0
Solution interval: 1, 7
−2
x 2 6x 8 ≥ 0
x 2 6x 9 < 16
x 2 6x 7 < 0
−1
x 3 2 ≥ 1
1 2 3 4 5
0 2 4 6
x 3x 1 > 0
Critical numbers:
x 1, x 7
1, 7 ⇒ x 1x 7 < 0
7, ⇒ x 1x 7 > 0
7
x 2 2x > 3
x 2 2x 3 > 0
8
x
Test intervals: , 3 ⇒ x 3x 1 > 0
Solution intervals: , 3 1,
−4 −3 −2 −1 0 1 2
x 2, x 4
2, 4 ⇒ x 2x 4 < 0
4, ⇒ x 2x 4 > 0
x
x 3, x 1
3, 1 ⇒ x 3x 1 < 0
1, ⇒ x 3x 1 > 0
x