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Intermediate Algebra , Ninth Edition PDF

783 Pages·2011·26.66 MB·English
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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

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Ideal for lecture-format courses taught at the post-secondary level, INTERMEDIATE ALGEBRA, Ninth Edition, makes algebra accessible and engaging. Author Charles "Pat" McKeague's passion for teaching mathematics is apparent on every page. With many years of experience teaching mathematics, he knows ho
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