NOT FOR SALESection P.1 Review of Real Nu mbers a nd Thei ection P.1 Review of Real Nu mbers a nd The INSTRUCTOR USE ONLY... The types of real numbers that may be used in a range of pri
Trang 18 5, 7, 73, 0, 3.12, ,54 3, 12, 5
(a) Natural numbers: 12, 5 (b) Whole numbers: 0, 12, 5 (c) Integers: 7, 0, 3, 12, 5(d) Rational numbers: 7, 73, 0, 3.12, ,54 3, 12, 5(e) Irrational numbers: 5
9 2.01, 0.666 , 13, 0.010110111 , 1, 6
(a) Natural numbers: 1 (b) Whole numbers: 1 (c) Integers: 13, 1, 6(d) Rational numbers: 2.01, 0.666 , 13, 1, 6(e) Irrational numbers: 0.010110111
25, 17, , 9, 3.12, S, 7, 11.1, 13(a) Natural numbers: 25, 9, 7, 13(b) Whole numbers: 25, 9, 7, 13(c) Integers: 25, 17, 9, 7, 13(d) Rational numbers:
12 5
25, 17, , 9, 3.12, 7, 11.1, 13(e) Irrational numbers: 12S
(c) The interval is unbounded
INSTRUCTOR USE ONLY
Trang 2Section P.1 Review of Real Nu mbers a nd Their P rop erties 3
18 (a) The inequality x denotes the set of all real 0
numbers less than zero
(b)
(c) The interval is unbounded
19 (a) The interval >4,f denotes the set of all real
numbers greater than or equal to 4
(b)
(c) The interval is unbounded
20 (a) f, 2 denotes the set of all real numbers less
than 2
(b)
(c) The interval is unbounded
21 (a) The inequality 2 x 2denotes the set of all
real numbers greater than 2 and less than 2
(b)
(c) The interval is bounded
22 (a) The inequality 0 x d denotes the set of all real 6
numbers greater than zero and less than or equal to 6
(b)
(c) The interval is bounded
23 (a) The interval >5, 2 denotes the set of all real
numbers greater than or equal to 5 and less than 2
(b)
(c) The interval is bounded
24 (a) The interval 1, 2@denotes the set of all real
numbers greater than and less than or equal to 2 1(b)
(c) The interval is bounded
NOT FOR SALESection P.1 Review of Real Nu mbers a nd Thei ection P.1 Review of Real Nu mbers a nd The
INSTRUCTOR USE ONLY
Trang 364 9 7x
(a) 9 7 3 9 21 30(b) 9 7 3 9 21 12
65 x2 5x 4(a) 2
(a) 1 1 2
Division by zero is undefined
68 x 3 x 3 0 Additive Inverse Property
69 2 x 3 2 3 and 6 2 3 14
12 3 4 and 12 3 4 110
30 5 6 and 30 5 6 1
INSTRUCTOR USE ONLY
Trang 22Section P.4 Factori ng Pol ynomi als 23
100 No, 3x 6 x 1 is not completely factored because 3x 6 3 x 2
Completely factored form is 3 x 2 x 1
103 Answers will vary Sample answer: x2 3
NOT FOR SALESection P.4 Factori ng Section P.4 Factori ng
INSTRUCTOR USE ONLY
Trang 235 The domain of the polynomial 3x2 4x is the set 7
of all real numbers
6 The domain of the polynomial 6x2 9,x ! is the set 0
of all positive real numbers because the polynomial is restricted to that set
set of all real numbers x such that x z 4
13 The domain of 4 x is the set of all real numbers x
Trang 24Section P.5 Rational Expressi ons 25
2 2 2
There are no common factors so this expression cannot
be simplified In this case, factors of terms were incorrectly cancelled
13
1
4 Undef
16
17
181
2
x
12
13
14
15
16
17
18
NOT FOR SALESection P.5 Rational Section P.5 Rationa
INSTRUCTOR USE ONLY
Trang 25... Standard form: 1 5
2x 14x
(b) Degree: Leading coefficient: 12(c) Binomial
(a) Standard form:... (c) Monomial
(a) Standard form: x6
(b) Degree: Leading coefficient: í1 (c) Binomial
8 (a) Standard form: 25y2... coefficient: 25 (c) Trinomial
9 (a) Standard form:
(b) Degree: Leading coefficient: (c) Monomial
10 (a) Standard form: t2 8(b) Degree:
Leading