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

228 Chapter 2 Polynomial and Rational Functions
33.
34.
35. y 1
36.
37.
y x 2 2x 3 (a)
6
−5 7
−2
y 1
2 x2 2x 1 (a)
−10
12
−4
8x3 1
2
8
−12 12
−8
x (a)
y x 3 x 2 16x 16 (a)
48
−12 12
−24
−2 −1 0 1 2
14
x
y ≤ 0 when x ≤ 1 or x ≥ 3.
(b) y ≥ 3 when 0 ≤ x ≤ 2.
y ≤ 0 (b) y ≥ 7
1
2 x2 2x 1 ≤ 0
x 2 4x 2 ≤ 0
x 4 ± 42 412
21
4 ± 8
2
y ≥ 0 when 2 ≤ x ≤ 0, 2 ≤ x < .
(b) y ≤ 6 when x ≤ 4.
2 ± 2
y ≤ 0 when 2 2 ≤ x ≤ 2 2.
y ≤ 0 (b)
x 3 x 2 16x 16 ≤ 0
x 2 x 1 16x 1 ≤ 0
x 1x 2 16 ≤ 0
y ≤ 0 when < x ≤ 4, 1 ≤ x ≤ 4.
Solution interval:
−1
0
1
4
1
4 ,
1
1
2 x2 2x 1 ≥ 7
x 2 4x 12 ≥ 0
x 6x 2 ≥ 0
y ≥ 36
Critical numbers:
Test intervals:
1 x
Test: Is
By testing an x-value in each test interval in the inequality,
we see that the solution set is: , 1 0, 1
2
1 x
x 0, x ±1
, 1, 1, 0, 0, 1, 1,
> 0?
x
2
> 0
x
1
x > 0
x
38.
Critical numbers: x 0, x
Test intervals: , 0 ⇒
1
0, 4 1
1 4x
< 0
x
4
1
4 < 0
x
y ≥ 7 when x ≤ 2, x ≥ 6.
x 3 x 2 16x 16 ≥ 36
x 3 x 2 16x 20 ≥ 0
x 2x 5x 2 ≥ 0
y ≥ 36 when x 2, 5 ≤ x < .
⇒ 1 4x
x
⇒ 1 4x
x
, 0 1
4 ,
x
1 4x
x
> 0
< 0
< 0