Intermediate Algebra , Ninth Edition

783 Pages·2011·26.66 MB·English

by  Charles P. McKeague

1019763_FM_VOL-I.qxp 9/17/07 4:22 PM Page viii
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
S 50
R 51
1st Pass Pages
Functions: A Summary
Paired Data Table Building
The foundation on which functions and graphs are We can build tables of paired data by using formulas
built is the study of paired data. Each row in Table 1 that contain two variables. Table 2 uses the formula
yields a pair of numbers that are related. For example, l = 6 − w to show the relationship between the length
a temperature of 25° on the Celsius scale is equivalent and width of a rectangle with a perimeter of 12 inches.
to 77° on the Fahrenheit scale. Figure 3 is a histogram constructed from the
information in the table.
TABLE 1
CorreSPonDinG TemPeraTureS TABLE 2
LenGTh anD wiDTh oF a reCTanGLe
Degrees Degrees
Celsius Fahrenheit width (in.) Length (in.)
w l = 6 − w l
0 32
25 77 1 l = 6 − 1 5
2 l = 6 − 2 4
50 122
3 l = 6 − 3 3
75 167
4 l = 6 − 4 2
100 212
5 l = 6 − 5 1
Bar Charts, Scatter Diagrams, and Line Graphs
5
5
Figure 1 shows a bar chart constructed from the
information in Table 1. The bar chart is a visual 4
4
description of the paired data in Table 1. The second
h 3
rectangle indicates that 25° C is the same as 77° F. ngt3
e
L 2
2
250
212 1
heit200 1
ahren150 167 1 2 3 4 5
es F 122 Width
Degre100 77 FigurE 3 A bar chart of Table 2.
50 32 Functions
Definition A function is a rule that pairs each
0 25 50 75 100 element in one set, called the domain, with exactly
Degrees Celsius
one element from a second set, called the range.
FigurE 1 A bar chart of Table 1.
With functions, we take numbers from the domain
Paired data can also be visualized with scatter and put them into the function rule. The function rule
diagrams, line graphs, and graphs drawn in a then outputs values in the range of the function. The
rectangular coordinate system. only restriction on this process is that each input can
have only one output. Here is a diagram that will help
y
visualize the relationship between the function rule
and the domain and range of the function.
250
heit 200 The Function Rule
n Domain: Range:
re The set of all inputs The set of all outputs
h 150
a
F
s
e 100
e
gr Example If you work from 0 to 40 hours per week
e
D 50 at a job that pays $7.50 per hour, then the amount
0 x of money you earn each week is a function of the
0 25 50 75 100 number of hours you work. If x is hours worked and y
Degrees Celsius
is weekly pay, then the function rule is
FigurE 2 A line graph of Table 1. y = 7.5x for 0 ≤ x ≤ 40
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
ordered Pairs Graphing Functions
A pair of numbers enclosed in parentheses and There are many ways to graph functions. Figure 6 is a
separated by a comma, such as (2, 1) is called an graph constructed by substituting 0, 10, 20, 30, and 40
ordered pair of numbers. The first number in the pair for x in the formula f(x) = 7.5x, and then using the
is called the x-coordinate of the ordered pair, while formula to find the corresponding values of y. Each
the second number is called the y-coordinate. For pair of numbers corresponds to a point in Figure 6.
the ordered pair (2, 1), the x-coordinate is 2 and the The points are connected with straight lines to form
y-coordinate is 1. the graph. y
The rectangular Coordinate System
350
We graph ordered pairs on a rectangular coordinate 300
system. A rectangular coordinate system is made by 250
drawing two real number lines at right angles to each $) 200
other. The two number lines, called axes, cross each Pay ( 150
other at 0. This point is called the origin. The
100
horizontal number line is the x-axis and the vertical
50
number line is the y-axis.
x
y
10 20 30 40 50
y-axis FigurE 6 The Hgroauprsh w oofr kfe(dx) = 7.5x, 0 ≤ x ≤ 40.
5
II I
4 Function notation
3
Positive The notation f(x) is used to denote elements in the
2 direction
range of a function. For example, if the rule for a
1
x function is given by y = 7.5x, then the rule can also be
−5−4−3−2−1 1 2 3 4 5 x-axis
−1 written as f(x) = 7.5x. If we ask for f(20), we are asking
Negative −2 Origin
direction −3 for the value of y that comes from x = 20. That is
III −4 IV if f(x) = 7.5x
−5
then f(20) = 7.5(20) = 150
Figure 7 is a diagram called a function map that
FigurE 4 The rectangular coordinate system.
gives a visual representation of this particular function:
Graphing ordered Pairs
Domain Rule: Multiply by 7.5 Range
To graph the ordered pair (a, b) on a rectangular
coordinate system, we start at the origin and move a 10 75
20 150
units right or left (right if a is positive and left if a is
x 7.5x
negative). We then move b units up or down (up if b is
FigurE 7 A function map.
positive and down if b is negative). The point where
we end up is the graph of the ordered pair (a, b). A function can also be thought of as a machine. We
Figure 5 shows the graphs of the ordered pairs (2, 5), put values of x into the machine which transforms
(−2, 5), (−2, −5), and (2, −5). them into values of f(x), which are then output by the
y machine. The diagram is shown in Figure 8.
(−2, 5) 5 (2, 5) Input x
4
3
Function
2
1
x
−5−4−3−2−1 1 2 3 4 5 Output f(x)
−1
−2
−3 FigurE 8 A function machine.
−4
We can organize our work with paired data, graphing,
(−2, −5) −5 (2, −5)
and functions into a more standard form by using
ordered pairs and the rectangular coordinate system.
FigurE 5 The graphs of four ordered pairs.
(Continued on inside back cover)
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
INtERMEDIatE
Ninth Edition
algEBRa
Charles P. McKeague
CuEsta CollEgE
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
This is an electronic version of the print textbook. Due to electronic rights
restrictions, some third party content may be suppressed. Editorial
review has deemed that any suppressed content does not materially
a ffect the overall learning experience. The publisher reserves the
right to remove content from this title at any time if subsequent
rights restrictions require it. For valuable information on pricing, previous
editions, changes to current editions, and alternate formats, please visit
w ww.cengage.com/highered to search by ISBN#, author, title, or keyword
for materials in your areas of interest.

Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
5522660099__0000__ffmm__ppii--ppxxxxvvii..iinndddd iiii 22//11//1100 1111::3377::4433 PPMM
Intermediate Algebra, Ninth Edition © 2012, 2008 Brooks/Cole, Cengage Learning
Charles P. McKeague
ALL RIGHTS RESERVED. No part of this work covered by the copyright herein
Acquisitions Editor: Marc Bove may be reproduced, transmitted, stored or used in any form or by any means
graphic, electronic, or mechanical, including but not limited to photocopying,
Developmental Editor: Carolyn Crockett
recording, scanning, digitizing, taping, Web distribution, information networks,
Assistant Editor: Shaun Williams or information storage and retrieval systems, except as permitted under
Editorial Assistant: Zachary Crockett Section 107 or 108 of the 1976 United States Copyright Act, without the prior
written permission of the publisher.
Media Editors: Heleny Wong, Guanglei Zhang
Marketing Manager: Gordon Lee
For product information and technology assistance, contact us at
Marketing Assistant: Angela Kim Cengage Learning Customer & Sales Support, 1-800-354-9706
Marketing Communications Manager: For permission to use material from this text or product,
Darlene Macanan submit all requests online at www.cengage.com/permissions
Further permissions questions can be emailed to
Content Project Manager: Jennifer Risden
[email protected]
Design Director: Rob Hugel
Art Director: Vernon Boes
Library of Congress Control Number: 2010933321
Print Buyer: Karen Hunt
ISBN-13: 978-0-8400-6420-2
Rights Acquisitions Specialist: Roberta Broyer
ISBN-10: 0-8400-6420-9
Production Service: XYZ Textbooks
Text Designer: Diane Beasley
Brooks/Cole
Photo Researcher: Bill Smith Group 20 Davis Drive
Copy Editor: Katherine Shields, XYZ Textbooks Belmont, CA 94002-3098
USA
Illustrator: Kristina Chung, XYZ Textbooks
Cover Designer: Irene Morris
Cengage Learning is a leading provider of customized learning solutions with
Cover Image: Pete McArthur
office locations around the globe, including Singapore, the United Kingdom,
Compositor: Donna Looper, XYZ Textbooks
Australia, Mexico, Brazil, and Japan. Locate your local office at:
www.cengage.com/global
Cengage Learning products are represented in Canada by Nelson E ducation, Ltd.
To learn more about Brooks/Cole, visit www.cengage.com/brookscole
Purchase any of our products at your local college store or at our preferred
online store www.cengagebrain.com
Printed in the United States of America
1 2 3 4 5 6 7 14 13 12 11 10
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
1019763_FM_VOL-I.qxp 9/17/07 4:22 PM Page viii
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
S 50
R 51
1st Pass Pages
Brief Contents
Chapter 1 Basic Properties and Definitions 1
Chapter 2 Equations and Inequalities in one Variable 69
Chapter 3 Equations and Inequalities in two Variables 131
Chapter 4 systems of linear Equations and Ineqaulities 223
Chapter 5 Exponents and Polynomials 277
Chapter 6 Rational Expressions and Rational Functions 349
Chapter 7 Rational Exponents and Roots 423
Chapter 8 Quadratic Functions 487
Chapter 9 Exponential and logarithmic Functions 555
Chapter 10 Conic sections 611
Chapter 11 sequences and series 645
Appendix A Introduction to Determinants 691
Appendix B Cramer’s Rule 697
Appendix C synthetic Division 701
Appendix D Conditional statements 705
answers to odd-Numbered Problems a-1
Index I-1

iii
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
1019763_FM_VOL-I.qxp 9/17/07 4:22 PM Page viii
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
S 50
R 51
1st Pass Pages