com xiii Our Commitment to Market Development and Accuracy Acknowledgments: Paramount to the development of College Algebra was the invaluable feedback provided by the instructors from around the country who reviewed the manuscript or attended a market development event over the course of the several years the text was in development. A Special Thanks to All of the Event Attendees Who Helped Shape College Algebra. Focus groups and symposia were conducted with instructors from around the country to provide feedback to editors and the authors and ensure the direction of the text was meeting the needs of students and instructors.

First and foremost, we want to thank our editor Emily Windelborn who started with us on this project when it was just idea, and then lent her unwavering, day-to-day support through final publication. To Ryan Blankenship, Marty Lange, and Kurt Strand, we are forever grateful for the amazing opportunities you and McGraw-Hill have given us. To our brand manager, Caroline Celano, as the pilot on this long journey you set the standard for leadership. Each day, you lead by example to unlock our full potential and inspire our best work. Thank you for making us shine. Our heartfelt gratitude goes to the production manager Peggy Selle for steering the ship and keeping us all on task. To Laurie Janssen and David Hash, many thanks for a beautiful design, and to Carrie Burger for the beautiful photos and art. The book is gorgeous. Special thanks to the digital team, Rob Brieler and Victor Pareja, for keeping the digital train on the tracks.

Thank you for overseeing the enormous job of managing digital content and ensuring consistency of the author voice. Along these lines, we must express our utmost gratitude to digital authors Alina Coronel, Esmarie Kennedy, Tim Chappell, Stephen Toner, Michael Larkin, Lizette Foley, Meghan Clovis, and Lance Gooden for their diligence writing digital content. All of you are amazing. To Jason Wetherington and Mary Beth Headlee, thank you so much for your work on SmartBook and for the additional pairs of eyes on our manuscript. To Beth Clickner, many, many thanks for the beautiful and thorough PowerPoint presentations of our material. To Nora Devlin, thank you for managing the solutions manual projects, lecture notes, and Internet Activities. No doubt, many instructors and students thank you as well. To Patricia Steele, the best copy editor ever, thank you for mentoring us and for ensuring consistency throughout our work. To Elka Block, Jennifer Blue, and the team at DiacriTech, many thanks for doing multiple levels of accuracy checking.

Your talents are absolutely amazing. Additional thanks to Julie Kennedy and Carey Lange for their tireless attention to detail proofreading pages. Finally, to the dedicated people in the McGraw-Hill sales force, thank you so much for your continued confidence, encouragement, and support. Most importantly, we want to give special thanks to all the students and instructors who use College Algebra in their classes. For example, a year-old with a maximum heart rate of beats per minute should strive for a target heart rate zone of between 98 and beats per minute. An introduction to modeling is presented here in Chapter R along with the standard order of operations used to carry out these calculations. Chapter R reviews skills and concepts required for success in college algebra. Just as an athlete must first learn the basics of a sport and build endurance and speed, a student studying mathematics must focus on necessary basic skills to prepare for the challenge ahead.

Preparation for algebra is comparable to an athlete preparing for a sporting event. Putting the time and effort into the basics here in Chapter R will be your foundation for success in later chapters. Identify Subsets of the Set of Real Numbers 1. Identify Subsets of the Set of A hybrid vehicle gets 48 mpg in city driving and 52 mpg on the highway. The formula A 5 c 1 h gives the amount of gas A in gal for c miles of city driving and h miles of highway driving. In the formula, A, c, and h are called variables and these represent values that are subject to change. The values and are called constants because their values do not change in the formula. For a trip from Houston, Texas, to Dallas, Texas, a motorist travels 36 mi of city driving and 91 mi of highway driving.

The amount of fuel used by this hybrid vehicle is given by 1 1 A5 1 48 52 5 2. Real Numbers Use Inequality Symbols and Interval Notation Find the Union and Intersection of Sets Evaluate Absolute Value Expressions Use Absolute Value to Represent Distance Apply the Order of Operations Simplify Algebraic Expressions Write Algebraic Models The numbers used in day-to-day life such as those used to determine fuel consumption come from the set of real numbers, denoted by R. A set is a collection of items called elements. The braces { and } are used to enclose the elements of a set. For example, {gold, silver, bronze} represents the set of medals awarded to the top three finishers in an Olympic event. A set that contains no elements is called the empty set or null set and is denoted by { } or [. Listing the elements in a set within braces is called the roster method. Using the roster method, the set of the even numbers between 0 and 10 is represented by {2, 4, 6, 8}. Another method to define this set is by using set-builder notation.

This uses a description of the elements of the set. For example, 5x Z x is an even number between 0 and The set of all x such that x is an even number between 0 and 10 In our study of college algebra, we will often refer to several important subsets parts of the set of real numbers Table R Table R-1 Subsets of the Set of Real Numbers, R Set TIP Notice that the first five letters of the word rational spell ratio. This will help you remember that a rational number is a ratio of integers. Examples: ratio of 26 and 11 and 9 ratio of 9 and 1. Examples: 0. Irrational numbers are real numbers that cannot be expressed as a ratio of integers.

The decimal form of an irrational number is nonterminating and nonrepeating. Examples: π and 12 Section R. It is important to realize that for nonterminating decimals, a calculator or spreadsheet will only give approximate values, not exact values. Real Numbers R Rational Numbers Integers Whole Numbers Irrational Numbers Natural Numbers Figure R-1 The relationships among the subsets of real numbers defined in Table R-1 are shown in Figure R In particular, notice that together the elements of the set of rational numbers and the set of irrational numbers make up the set of real numbers. EXAMPLE 1 Identifying Elements of a Set Given A 5 E 13, 0.

Solution: a. B 5 E, , 4. Use Inequality Symbols and Interval Notation All real numbers can be located on the real number line. We say that a is less than b written symbolically as a , b if a lies to the left of b on the number line. This is equivalent to saying that b is greater than a written symbolically as b. a because b lies to the right of a. a b a , b is equivalent to b. a Answers 1. However, finding taxable income is not always trivial. There are numerous variables that come into play. The IRS takes into account exemptions, deductions, and tax credits among Schedule X—If your filling status is Single other things. Source: Internal Revenue Service, www.

gov Chapter 2 Functions and Relations SECTION 2. Therefore, it is important to learn how to create and interpret meaningful graphs. Understanding how points are located relative to a fixed origin is important for many graphing applications. For example, computer game developers use a rectangular coordinate system to define the locations of objects moving around the screen. Plot Points on a Rectangular Coordinate System 2. Use the Distance and Midpoint Formulas 3. Graph Equations by Plotting Points 4. Identify x- and y-Intercepts 5. Graph Equations Using a 1. He did this by intersecting two perpendicular number lines with the point of intersection called the origin. These lines form a rectangular coordinate system also known in his honor as the Cartesian coordinate system or simply a coordinate plane. The horizontal line is called the x-axis and the vertical line is called the y-axis.

The x- and y-axes divide the plane into four quadrants. The quadrants are labeled counterclockwise as I, II, III, and IV Figure Every point in the plane can be uniquely identified by using an ordered pair x, y to specify its coordinates with respect to the origin. In an ordered pair, the first coordinate is called the x-coordinate, and the second is called the y-coordinate. The origin is identified as 0, 0. In Figure , six points have been graphed. The point 23, 5 , for example, is placed 3 units in the negative x direction to the left and 5 units in the positive y direction upward. Use the Distance and Midpoint Formulas 4, 9 8 3 4 Quadrant IV Figure 10 9 23, 5 x, y 5 2.

Now we want to find the distance between two points in a coordinate plane. For example, consider the points 1, 5 and 4, 9. The distance d between the points is labeled in Figure The dashed horizontal and vertical line segments form a right triangle with hypotenuse d. The horizontal distance between the points is 4 2 [email protected] 5 3. The vertical distance between the points is 9 2 5 5 4. Section 2. The distance between the points is 5 units. We can make this process generic by labeling the points P x1, y1 and Q x2, y2. See Figure Applying the Pythagorean theorem, we have d 2 5 x2 2 x1 2 1 y2 2 y1 2 d 5 2 x2 2 x1 1 y2 2 y1 2 TIP Since x2 2 x1 2 5 x1 2 x2 2 and y2 2 y1 2 5 y1 2 y2 2, the distance formula can also be expressed as 2 We can drop the absolute value bars because 0 a 0 2 5 a 2 for all real numbers a.

Distance Formula The distance between points x1, y1 and x2, y2 is given by d 5 2 x2 2 x1 2 1 y2 2 y1 2 d 5 2 x1 2 x2 2 1 y1 2 y2 2. EXAMPLE 1 Finding the Distance Between Two Points Find the distance between the points 25, 1 and 7, Give the exact distance and an approximation to 2 decimal places. Solution: 25, 1 and 7, 23 x1, y1 and x2, y2 Label the points. Note that the choice for x1, y1 and x2, y2 will not affect the outcome. d 5 2[7 2 25 ]2 1 23 2 1 2 Apply the distance formula. The exact distance is 4 units. This is approximately However, in the case of the Pythagorean theorem, the converse is a true statement. Answer 1. The Pythagorean theorem tells us that if a right triangle has legs of lengths a and b and hypotenuse of length c, then a2 1 b2 5 c2. The following related statement is also true: If a2 1 b2 5 c2, then a triangle with sides of lengths a, b, and c is a right triangle. We use this important concept in Example 2. Solution: TIP We denote the distance between points P and Q as d P, Q or PQ.

The second notation is the length of the line segment with endpoints P and Q. y Determine the distance between each pair of points. Label the shorter sides as a and b. Check the condition that a2 1 b2 5 c2. y x2, y2 x1 1 x2 , y1 1 y2 2 2 x1, y1 Now suppose that we want to find the midpoint of the line segment between the distinct points x1, y1 and x2, y2. The midpoint of a line segment is the point equidistant the same distance from the endpoints Figure The x-coordinate of the midpoint is the average of the x-coordinates from the endpoints. Likewise, the y-coordinate of the midpoint is the average of the y-coordinates from the endpoints.

x Figure Midpoint Formula The midpoint of the line segment with endpoints x1, y1 and x2, y2 is M5a x1 1 x2 y1 1 y2 , b 2 2 average of x-coordinates EXAMPLE 3 Avoiding Mistakes average of y-coordinates The midpoint of a line segment is an ordered pair with two coordinates , not a single number. Finding the Midpoint of a Line Segment Find the midpoint of the line segment with endpoints 4. y Solution: Answer 2. Apply the midpoint formula. Graph Equations by Plotting Points The relationship between two variables can often be expressed as a graph or expressed algebraically as an equation. For example, suppose that two variables, x and y, are related such that y is 2 more than x. An equation to represent this relationship is y 5 x 1 2. A solution to an equation in the variables x and y is an ordered pair x, y that when substituted into the equation makes the equation a true statement.

For example, the following ordered pairs are solutions to the equation y 5 x 1 2. The graph of all solutions to an equation is called the graph of the equation. The graph of y 5 x 1 2 is shown in Figure One of the goals of this text is to identify families of equations and the characteristics of their graphs. As we proceed through the text, we will develop tools to graph equations efficiently. For now, we present the point-plotting method to graph the solution set of an equation. In Example 4, we start by selecting several values of x and using the equation to calculate the corresponding values of y. Then we plot the points to form a general outline of the curve. EXAMPLE 4 Graphing an Equation by Plotting Points Graph the equation by plotting points. Then use the equation to calculate the corresponding y values. Therefore, the values of x must be chosen so that when substituted into the equation, they produce a real number for y. Sometimes the values of x must be restricted to produce real numbers for y.

This is demonstrated in Example 5. EXAMPLE 5 Graphing an Equation by Plotting Points Graph the equation by plotting points. Apply the square root property. y TIP x In Example 5, we choose several convenient values of x such as 21, 0, 3, and 8 so that the radicand will be a perfect square. Identify x- and y-Intercepts y When analyzing graphs, we want to examine their most important features. Two key features are the x- and y-intercepts of a graph. These are the points where a graph intersects the x- and y-axes. Any point on the x-axis has a y-coordinate of zero. Therefore, an x-intercept is a point a, 0 where a graph intersects the x-axis Figure Any point on the y-axis has an x-coordinate of zero.

Therefore, a y-intercept is a point 0, b where a graph intersects the y-axis Figure For example, if an x-intercept is 24, 0 , then the x-intercept may be stated simply as 24 the y-coordinate is understood to be zero. Similarly, we may refer to a y-intercept as the y-coordinate of a point of intersection that a graph makes with the y-axis. For example, if a y-intercept is 0, 2 , then it may be stated simply as 2. Answer y 5. x1 y2 52 To find the x- and y-intercepts from an equation in x and y, follow these steps. Find the x-intercept s. Find the y-intercept s. y 0 0x0 x 5 5 5 5 0x0 2 1 0x0 2 1 1 1 or x 5 21 To find the x-intercept s , substitute 0 for y and solve for x. Isolate the absolute value. Recall that for k.

The x-intercepts are 1, 0 and 21, 0. The y-intercept is 0, The intercepts 1, 0 , 21, 0 , and 0, 21 are consistent with the graph of the equation y 5 0 x 0 2 1 found in Example 4 Figure Skill Practice 6 Given the equation y 5 x2 2 4, a. TIP Sometimes when solving for an x- or y-intercept, we encounter an equation with an imaginary solution. In such a case, the graph has no x- or y-intercept. Graph Equations Using a Graphing Utility Answers 6. We will quickly enhance this method with other techniques that are less cumbersome and use more analysis and strategy. One weakness of the point-plotting method is that it may be slow to execute by pencil and paper. Also, the selected points must fairly represent the shape of the graph. Otherwise the sketch will be inaccurate. Graphing utilities can help with both of these weaknesses. They can graph many points quickly, and the more points that are plotted, the greater the likelihood that we see the key features of the graph.

Graphing utilities include graphing calculators, spreadsheets, specialty graphing programs, and apps on phones. Figures and show a table and a graph for y 5 x2 2 3. Notice that the calculator expects the equation represented with the y variable isolated. To set up a table, enter the starting value for x, in this case, Then set the increment by which to increase x, in this case 1. Figure The table shows eleven x-y pairs but more can be accessed by using the up and down arrow keys on the keypad. In this context, it represents the change from one value of x to the next. The graph in Figure is shown between x and y values from to The tick marks on the axes are 1 unit apart. The viewing window with these parameters is denoted [, 10, 1] by [, 10, 1].

minimum x value TIP The calculator plots a large number of points and then connects the points. So instead of graphing a single smooth curve, it graphs a series of short line segments. This may give the graph a jagged look Figure maximum x value minimum y value maximum y value 10 [, 10, 1] by [, 10, 1]. Solution: Enter the equations using the Y5 editor. Use the WINDOW editor to change the viewing window parameters. The variables Xmin, Xmax, and Xscl relate to [, 20, 2]. The variables Ymin, Ymax, and Yscl relate to [, 15, 3]. Notice that the graphs of both equations appear. This provides us with a tool for visually examining two different models at the same time.

Simplify the radical. Solve for y. ax 1 by 5 c Evaluate x2 1 4x 1 5 for x 5 25 Concept Connections 1. In a rectangular coordinate system, the point where the x- and y-axes meet is called the 2. The x- and y-axes divide the coordinate plane into four regions called. The distance between two distinct points x1, y1 and x2, y2 is given by the formula. The midpoint of the line segment with endpoints x1, y1 and x2, y2 is given by the formula 5. to an equation in the variables x and y is an ordered pair x, y that makes the equation a true statement. An x-intercept of a graph has a y-coordinate of. A y-intercept of a graph has an x-coordinate of. Given an equation in the variables x and y, find the y-intercept by substituting for x and solving for Objective 1: Plot Points on a Rectangular Coordinate System For Exercises 9—10, plot the points on a rectangular coordinate system. Find the exact distance between the points. See Example 1 b. Find the midpoint of the line segment whose endpoints are the given points.

See Example 3 A 15, 2 12B and A, B A 17, B and A, 15B. See Example 2 See Examples 4—5 y 5 0 x 2 2 0 Objective 4: Identify x- and y-Intercepts For Exercises 45—50, estimate the x- and y-intercepts from the graph. See Example 6 A map of a wilderness area is drawn with the origin placed at the parking area. Two fire observation platforms are located at points A and B. If a fire is located at point C, determine the distance to the fire from each observation platform. A map of a state park is 5 drawn so that the origin is 4 placed at the visitor center. Suppose that 1 two hikers are located at 25 24 23 22 21 21 points A and B. Determine the distance 23 between the hikers. If the hikers want to meet for lunch, determine the location of the midpoint between the hikers.

The coordinates of the ordered pair give the number of pixels horizontally and vertically from the origin. Use this scenario for Exercises 65— Suppose that player A is located at 36, and player B is located at , How far apart are the players? Round to the nearest pixel. If the two players move directly toward each other at the same speed, where will they meet? If player A moves three times faster than player B, where will they meet? Verify that the points A 0, 0 , B x, 0 , and C a x, 2 2 make up the vertices of an equilateral triangle. Suppose that a player is located at point A , and must move in a direct line to point B 80, and then in a direct line to point C , 60 to pick up prizes before a 5-sec timer runs out. If the player moves at pixels per second, will the player have enough time to pick up both prizes? Verify that the points A 0, 0 , B x, 0 , and C 0, x make up the vertices of an isosceles right triangle an isosceles triangle has two sides of equal length. For Exercises 69—70, assume that the units shown in the grid are in feet.

Determine the exact length and width of the rectangle shown. Determine the perimeter and area. Find the center and radius of the circle. Find the area of the triangle. Assume that the units shown in the grid are in meters. Three points are collinear if they all fall on the same line. There are several ways that we can determine if three points, A, B, and C are collinear. One method is to determine if the sum of the lengths of the line segments AB and BC equals the length of AC. Suppose that d represents the distance between two points x1, y1 and x2, y2. Explain how the distance formula is developed from the Pythagorean theorem. Explain how you might remember the midpoint formula to find the midpoint of the line segment between x1, y1 and x2, y2. Explain how to find the x- and y-intercepts from an equation in the variables x and y. Given an equation in the variables x and y, what does the graph of the equation represent?

z Expanding Your Skills A point in three-dimensional space can be represented in a three-dimensional coordinate system. In such a case, a z-axis is taken perpendicular to both the x- and y-axes. A point P is assigned an ordered triple P x, y, z relative to a fixed origin where the three axes meet. For Exercises 83—86, determine the distance between the two given points in space. What is meant by a viewing window on a graphing device? Which of the viewing windows would show both the x- and y-intercepts of the graph of x 2 42y 5 ? See Example 7 y 5 2x 2 5 on [, 10, 1] by [, 10, 1] y 5 24x 1 1 on [, 10, 1] by [, 10, 1] y 5 x2 2 x on [25, 5, 1] by [, , ] y 5 x2 1 x on [25, 5, 1] by [, , ] For Exercises 93—94, graph the equations on the standard viewing window.

Write an Equation of a Circle in Standard Form 1. Write an Equation of a Circle In addition to graphing equations by plotting points, we will learn to recognize specific categories of equations and the characteristics of their graphs. We begin by presenting the definition of a circle. in Standard Form 2. Write the General Form of an Equation of a Circle Definition of a Circle A circle is the set of all points in a plane that are equidistant from a fixed point called the center. The fixed distance from any point on the circle to the center is called the radius. y r x, y h, k x Figure The radius of a circle is often denoted by r, where r.

It is also important to note that the center is not actually part of the graph of a circle. It will be drawn in the text as an open dot for reference only. Suppose that a circle is centered at the point h, k and has radius r Figure The distance formula can be used to derive an equation of the circle. Let x, y be an arbitrary point on the circle. Then by definition the distance between h, k and x, y must be r. Apply the distance formula. EXAMPLE 1 Writing an Equation of a Circle in Standard Form a. Write the standard form of an equation of the circle with center 24, 6 and radius 2. Graph the circle. Point of Interest Solution: Among his many contributions to mathematics, René Descartes discovered analytic geometry, which uses algebraic equations to describe geometric shapes.

For example, a circle can be described by the algebraic equation x 2 h 2 1 y 2 k 2 5 r 2. Standard form: x 2 h 2 1 y 2 k 2 5 r2 Simplify. To graph the circle, first locate the center and draw a small open dot. Then plot points r units to the left, right, above, and below the center. Draw the circle through the points. Write an equation of the circle with center 3, 21 and radius 4. EXAMPLE 2 Write the standard form of an equation of the circle with endpoints of a diameter 21, 0 and 3, 4. Answers 1. Solution: 4 3 2 1 22 21 21 22 23 24 25 26 Writing an Equation of a Circle in Standard Form A sketch of this scenario is given in Figure Notice that the midpoint of the diameter is the center of the circle.

Using the endpoint 21, 0 as x1, y1 and the center 1, 2 as x2, y2 , apply the distance formula. Write the General Form of an Equation of a Circle In Example 2 we have the equation x 2 1 2 1 y 2 2 2 5 8. If we expand the binomials and combine like terms, we can write the equation in general form. x 2 1 2 1 y 2 2 2 5 8 x2 2 2x 1 1 1 y2 2 4y 1 4 5 8 x2 1 y2 2 2x 2 4y 2 3 5 0 Standard form center-radius form Expand the binomials General form General Form of an Equation of a Circle An equation of a circle written in the form x2 1 y2 1 Ax 1 By 1 C 5 0 is called the general form of an equation of a circle. By completing the square we can write an equation of a circle given in general form as an equation in standard form.

The purpose of writing an equation of a circle in standard form is to identify the radius and center. This is demonstrated in Example 3. EXAMPLE 3 Writing an Equation of a Circle in Standard Form Write the equation of the circle in standard form. Then identify the center and radius. Group the y terms. Move the constant term to the right. Complete the squares. The center is 25, 3 , and the radius is 19 5 3. Skill Practice 3 Write the equation of the circle in standard form. x2 1 y2 2 8x 1 2y 2 8 5 0 Not all equations of the form x2 1 y2 1 Ax 1 By 1 C 5 0 represent the graph of a circle. Completing the square results in an equation of the form x 2 h 2 1 y 2 k 2 5 c, where c is a constant. In the case where c.

However, if c 5 0, or if c , 0, the graph will be a single point or nonexistent. These are called degenerate cases. The solution set is { h, k }. EXAMPLE 4 Determining if an Equation Represents the Graph of a Circle Write the equation in the form x 2 h 2 1 y 2 k 2 5 r2, and identify the solution set. Note that the x2 term is already a perfect square: x 2 0 2. Complete the square: C 12 D 2 5 Since r2 5 0, the solution set is { 0, 7 }. The sum of two squares will equal zero only if each individual term is zero. Therefore, x 5 0 and y 5 7. Skill Practice 4 Write the equation in the form x 2 h 2 1 y 2 k 2 5 r2, and identify the solution set.

Therefore, to graph an equation of a circle such as x 1 5 2 1 y 2 3 2 5 9, from Example 3, we first solve for y. This is because the calculator has a rectangular screen. If the scaling is the same on the x- and y-axes, the graph will appear elongated horizontally. To eliminate this distortion, use a ZSquare option, located in the Zoom menu. Answer 4. The viewing window between x 5 These may not include x values at the leftmost and rightmost points on the circle. That is, the calculator may graph points close to 28, 3 and 22, 3 but not exactly at 28, 3 and 22, 3. Then factor the trinomial. Find the distance between 2, 3 and 23, Multiply by using the special case products. Express your answer in simplified radical form. x 2 2 2 Concept Connections 1. A is the set of all points in a plane equidistant from a fixed point called the 2.

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English Pages pages [] Year , DOWNLOAD PDF FILE. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students, this text's com. Learn to think mathematically and develop genuine problem-solving skills with COLLEGE ALGEBRA, Seventh Edition. This str. Learn to think mathematically and develop genuine problem-solving skills with Stewart, Redlin, and Watson's COLLEGE. James Stewart, author of the worldwide, best-selling Calculus texts, along with two of his former Ph. students, Lothar. New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added througho. This is a pre historical reproduction that was curated for quality. Quality assurance was conducted on each of thes. Julie Miller Daytona State College Digital contributions from Donna Gerken Miami-Dade College Kendall COLLEGE ALGEBRA, SECOND EDITION Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY Copyright © by McGraw-Hill Education.

All rights reserved. Printed in the United States of America. Previous editions © No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. Selle Assessment Content Project Manager: Eric Dosmann Buyer: Jennifer Pickel Design: David W. Typeface: Times LT Std. Printer: R. Donnelley All credits appearing on page or at the end of the book are considered to be an extension of the copyright page. pages cm Includes index. ISBN —0—07——4 alk. paper — ISBN 0—07——0 alk.

paper — ISBN —1———9 alk. paper — ISBN 1———0 alk. paper 1. Gerken, Donna. M54 The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites. com About the Authors Julie Miller is from Daytona State College where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at DSC, she worked as a software engineer for General Electric in the area of flight and radar simulation.

Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored textbooks in developmental mathematics, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers. I remember doing simple calculations with him and using graph paper to plot data points for his experiments. He would then tell me what the peaks and features in the graph meant in the context of his experiment. Throughout her career she has been actively involved with many projects at Miami Dade including those on computer learning, curriculum design, and the use of technology in the classroom. Letter from the Authors For many students, college algebra serves as a gateway course to the higher levels of mathematics needed for a variety of careers.

Our goal is to offer every student an opportunity for success in college algebra by bringing together a seamless integration of print and digital content delivery. The clear, concise writing style and pedagogical features of our textbook continue throughout the online content in ConnectMath, in our instructional videos, and in the adaptive reading and learning experience of SmartBook. Julie Miller donna gerken Dedications [email protected] [email protected] o my parents Kent and Joanne Miller who have always taught me the value of education. Through her friendly and engaging writing style, students are able to understand the material easily.

These exercises are linked to examples in the text and direct students to similar problems whose solutions have been stepped-out in detail. They can be easily skipped for those who do not encourage the use of calculators. Problem Recognition Exercises Problem Recognition Exercises appear in strategic locations in each chapter of the text. These exercises provide students with an opportunity to synthesize multiple concepts and decide which problem-solving technique to apply to a given problem. These exercises are highlighted with blue circles in the exercise sets and mirror the related examples.

With increased demands on faculty time, this has been a popular feature that helps faculty write their lectures and develop their presentation of material. If an instructor presents all of the highlighted exercises, then each objective of that section of text will be covered. Modeling and Applications One of the most important tools to motivate our students is to make the mathematics they learn meaningful in their lives. The textbook is filled with robust applications and numerous opportunities for mathematical modeling for those instructors looking to incorporate these features into their course. Callouts Throughout the text, popular tools are included to highlight important ideas. Avoiding Mistakes boxes that fend off common mistakes.

Point of Interest boxes that offer interesting and historical mathematical facts. Instructor Notes to assist with lecture preparation. vii Graphing Calculator Coverage Material is presented throughout the book illustrating how a graphing utility can be used to view a concept in a graphical manner. The goal of the calculator material is not to replace algebraic analysis, but rather, to enhance understanding with a visual approach. Graphing calculator examples are placed in self-contained boxes and may be skipped by instructors who choose not to implement the calculator. Similarly, the graphing calculator exercises are found at the end of the exercise sets and may also be easily skipped. A detailed summary is located at www. Chapter review exercises. Chapter test. Cumulative review exercises. These exercises cover concepts in the current chapter as well as all preceding chapters. These allow students to ensure they have the necessary foundational skills to be successful in the section.

For the first time, SmartBook is now available within Connect Math Hosted by ALEKS. This has also been updated in all of the digital materials accompanying the text. viii Key Features Supplement Package Supplements for the Instructor Author-Created Digital Media Digital assets were created exclusively by the author team to ensure that the author voice is present and consistent throughout the supplement package. The animations are diverse in scope and give students an interactive approach to conceptual learning. The animated content illustrates difficult concepts by leveraging the use of on-screen movement where static images in the text may fall short. They are organized in Connect hosted by ALEKS by chapter and section. The IRM includes Guided Lecture Notes, Classroom Activities using Wolfram Alpha, and Group Activities.

The notes step through the material with a series of questions and exercises that can be used in conjunction with lecture. The steps shown in the solutions match the style and methodology of solved examples in the textbook. TestGen is a computerized test bank utilizing algorithmbased testing software to create customized exams quickly. This user-friendly program enables instructors to search for questions by topic, format, or difficulty level; to edit existing questions, or to add new ones; and to scramble questions and answer keys for multiple versions of a single test. Hundreds of text-specific, open-ended, and multiple-choice questions are included in the question bank.

Power Points present key concepts and definitions with fully editable slides that follow the textbook. An instructor may project the slides in class or post to a website in an online course. Supplements for the Student Student Worksheets including guided lecture notes that step through the key objectives and Problem Recognition Exercise worksheets. ALEKS® Prep for College Algebra ALEKS Prep for College Algebra focuses on prerequisites and introductory material for College Algebra. These prep products can be used during the first 3 weeks of a course to prepare students for future success in the course and to increase retention and pass rates.

Connect Math® Hosted by ALEKS Connect Math Hosted by ALEKS Corp. is an exciting, new assignment and assessment ehomework platform. Starting with an easily viewable, intuitive interface, students will be able to access key information, complete homework assignments, and utilize an integrated, mediarich eBook. Smartbook® is the first and only adaptive reading experience available for the higher education market. As a student reads, the material continously adapts to ensure the student is focused on the content he or she needs the most to close specific knowledge gaps. Detailed Chapter Summaries are available at www. ix Efficient. Easy to Use. Gives Your Students the ALEKS Advantage Are your students prepared for your course? Do they learn at different paces? Is there inconsistency between homework and test scores? ALEKS successfully addresses these core challenges and more.

With decades of scientific research behind its creation, ALEKS offers the most advanced adaptive learning technology that is proven to increase student success in math.

Apply the distance formula. In this context, it represents the change from one value of x to the next. See Example 5 In Figure , six points have been graphed. Use the graph to find the solution set to the inequality 3x 2 x 1 4 2 1 0. B 5 E, , 4. EXAMPLE 2 Determining if a Relation Is a Function Determine if the relation defines y as a function of x.

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