Using authentic data to make math meaningful to students, **Jay Lehmann’s algebra series** uses a curve-fitting approach to model compelling, real-world situations, while answering the perennial question “But what is this good for?” Beginning with interesting data sets, students are asked to find models and derive equations to fit a scenario, helping them to understand functions graphically, numerically, and symbolically. Updated exercises, labs, and graphs deepen students’ understanding of core concepts and keeps them motivated to learn.

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0321868196 / 9780321868190 Intermediate Algebra: Functions & Authentic Applications

For more than twenty years, **Jay Lehmann** has taught at College of San Mateo, where he has received the Shiny Apple Award for excellence in teaching. He has worked on a NSF-funded grant to study classroom assessment and has performed research on collaborative directed-discovery learning. Jay has served as the newsletter editor for CMC3 (California Mathematics Council, Community College) for twelve years. He has presented at more than seventy-five conferences, including AMATYC, ICTCM, and T3, where he has discussed curve fitting and sung his "Number Guy" song.

Jay plays in a rock band called The Procrastinistas, who play at various clubs in the San Francisco Bay Area, where Jay, his wife Keri, and son Dylan reside. He plays a number of instruments including bass, guitar, piano, violin, and baritone. In addition to his elementary, intermediate, and combined algebra textbooks, Jay is currently writing a heist novel for high school students, which he hopes will be published before Dylan outgrows it. Dylan, a devoted drummer and artist, drafted many of the cartoons that are included in Jay's textbooks.

**In the words of the author:**

Before writing my algebra series, it was painfully apparent that my students couldn't relate to the applications in the course. I was plagued with the question, "What is this good for?" To try to bridge that gap, I wrote some labs, which facilitated my students in collecting data, finding models via curve fitting, and using the models to make estimates and predictions. My students really loved working with the current, compelling, and authentic data and experiencing how mathematics truly is useful.

My students' response was so strong that I decided to write an algebra series. Little did I know that to realize this goal, I would need to embark on a 15-year challenging journey, but the rewards of hearing such excitement from students and faculty across the country has made it all worthwhile! I'm proud to have played even a small role in raising peoples' respect and enthusiasm for mathematics.

have tried to honor my inspiration: by working with authentic data, students can experience the power of mathematics. A random-sample study at my college suggests that I am achieving this goal. The study concludes that students who used my series were more likely to feel that mathematics would be useful in their lives (P-value 0.0061) as well as their careers (P-value 0.024).

The series is excellent preparation for subsequent courses; in particular, because of the curve fitting and emphasis on interpreting the contextual meaning of parameters, it is an ideal primer for statistics. In addition to curve fitting, my approach includes other types of meaningful modeling, directed-discovery explorations, conceptual questions, and of course, a large bank of skill problems. The curve-fitting applications serve as a portal for students to see the usefulness of mathematics so that they become fully engaged in the class. Once involved, they are more receptive to all aspects of the course.

Preface

To The Student

Acknowledgments

Index of Applications

**1. Linear Equations and Linear Functions**

1.1 Using Qualitative Graphs to Describe Situations

1.2 Graphing Linear Equations

1.3 Slope of a Line

1.4 Meaning of Slope for Equations, Graphs, and Tables

1.5 Finding Linear Equations

1.6 Functions

Chapter Summary

Key Points of Chapter 1

Chapter 1 Review Exercises

Chapter 1 Test

**2. Modeling With Linear Functions**

2.1 Using Lines to Model Data

2.2 Finding Equations of Linear Models

2.3 Function Notation and Making Predictions

2.4 Slope Is a Rate of Change

Taking It to the Lab: Climate Change Lab * Used Car Lab * Golf

Ball Lab * Walking Student Lab * Linear Model Lab: Topic of Your

Choice

Chapter Summary

Key Points of Chapter 2

Chapter 2 Review Exercises

Chapter 2 Test

**3. Systems of Linear Equations**

3.1 Using Graphs and Tables to Solve Systems

3.2 Using Substitution and Elimination to Solve Systems

3.3 Using Systems to Model Data

3.4 Value, Interest, and Mixture Problems

3.5 Using Linear Inequalities in One Variable to Make Predictions

3.6 Linear Inequalities in Two Variables; Systems of Linear Inequalities

Taking It to the Lab: Climate Change Lab * Sports Lab * Truck Lab

Chapter Summary

Key Points of Chapter 3

Chapter 3 Review Exercises

Chapter 3 Test

Cumulative Review of Chapters 1—3

**4. Exponential Functions**

4.1 Properties of Exponents

4.2 Rational Exponents

4.3 Graphing Exponential Functions

4.4 Finding Equations of Exponential Functions

4.5 Using Exponential Functions to Model Data

Taking It to the Lab: Stringed Instrument Lab * Cooling Water

Lab * Exponential Lab: Topic of Y our Choice

Chapter Summary

Key Points of Chapter 4

Chapter 4 Review Exercises

Chapter 4 Test

**5. Logarithmic Functions**

5.1 Composite Functions

5.2 Inverse Functions

5.3 Logarithmic Functions

5.4 Properties of Logarithms

5.5 Using the Power Property with Exponential Models to Make Predictions

5.6 More Properties of Logarithms

5.7 Natural Logarithms

Taking It to the Lab: China and India Populations Lab

Folding Paper Lab

Exponential/Logarithmic Lab: Topic of Your Choice

Chapter Summary

Key Points of Chapter 5

Chapter 5 Review Exercises

Chapter 5 Test

Cumulative Review of Chapters 1—5

**6. Polynomial Functions**

6.1 Adding and Subtracting Polynomial Expressions and Functions

6.2 Multiplying Polynomial Expressions and Functions

6.3 Dividing Polynomials: Long Division and Synthetic Division

6.4 Factoring Trinomials of the Form *x*^{2} + bx + c; Factoring Out the GCF

6.5 Factoring Polynomials

6.6 Factoring Special Binomials; A Factoring Strategy

6.7 Using Factoring to Solve Polynomial Equations

Taking It to the Lab: Climate Change Lab * Projectile Lab

Chapter Summary

Key Points of Chapter 6

Chapter 6 Review Exercises

Chapter 6 Test

**7. Quadratic Functions**

7.1 Graphing Quadratic Functions in Vertex Form

7.2 Graphing Quadratic Functions in Standard Form

7.3 Using the Square Root Property to Solve Quadratic Equations

7.4 Solving Quadratic Equations by Completing the Square

7.5 Using the Quadratic Formula to Solve Quadratic Equations

7.6 Solving Systems of Linear Equations in Three Variables; Finding Quadratic Functions

7.7 Finding Quadratic Models

7.8 Modeling with Quadratic Functions

Taking It to the Lab: Climate Change Lab

Projectile Lab

Projectile Lab (Using a CBR or CBL)

Water Flow Lab

Quadratic Lab: Topic of Your Choice

Chapter Summary

Key Points of Chapter 7

Chapter 7 Review Exercises

Chapter 7 Test

Cumulative Review of Chapters 1—7

**8. Rational Functions**

8.1 Finding the Domains of Rational Functions and Simplifying Rational Expressions

8.2 Multiplying and Dividing Rational Expressions; Converting Units

8.3 Adding and Subtracting Rational Expressions

8.4 Simplifying Complex Rational Expressions

8.5 Solving Rational Equations

8.6 Modeling with Rational Functions

8.7 Variation

Taking It to the Lab: Climate Change Lab * Illumination

Lab * Boyle’s Law Lab

Chapter Summary

Key Points of Chapter 8

Chapter 8 Review Exercises

Chapter 8 Test

**9. Radical Functions**

9.1 Simplifying Radical Expressions

9.2 Adding, Subtracting, and Multiplying Radical Expressions

9.3 Rationalizing Denominators and Simplifying Quotients of Radical Expressions

9.4 Graphing and Combining Square Root Functions

9.5 Solving Radical Equations

9.6 Modeling with Square Root Functions

Taking It to the Lab: Pendulum Lab

Chapter Summary

Key Points of Chapter 9

Chapter 9 Review Exercises

Chapter 9 Test

**10. Sequences and Series**

10.1 Arithmetic Sequences

10.2 Geometric Sequences

10.3 Arithmetic Series

10.4 Geometric Series

Taking It to the Lab: Bouncing Ball Lab * Stacked Cups Lab

Chapter Summary

Key Points of Chapter 10

Chapter 10 Review Exercises

Chapter 10 Test

Cumulative Review of Chapters 1—10

**11. Additional Topics**

11.1 Absolute Value: Equations and Inequalities

Key Points of Section 11.1

11.2 Performing Operations with Complex Numbers

Key Points of Section 11.2

11.3 Pythagorean Theorem, Distance Formula, and Circles

Key Points of Section 11.3

11.4 Ellipses and Hyperbolas

Key Points of Section 11.4

11.5 Solving Nonlinear Systems of Equations

Key Points of Section 11.5

**A. Reviewing Prerequisite Material**

A.1 Plotting Points

A.2 Identifying Types of Numbers

A.3 Absolute Value

A.4 Performing Operations with Real Numbers

A.5 Exponents

A.6 Order of Operations

A.7 Constants, Variables, Expressions, and Equations

A.8 Distributive Law

A.9 Combining Like Terms

A.10 Solving Linear Equations in One Variable

A.11 Solving Equations in Two or More Variables

A.12 Equivalent Expressions and Equivalent Equations

**B. Using a TI-83 or TI-84 Graphing Calculator (available online)**

B.1 Turning a Graphing Calculator On or Off

B.2 Making the Screen Lighter or Darker

B.3 Entering an Equation

B.4 Graphing an Equation

B.5 Tracing a Curve without a Scattergram

B.6 Zooming

B.7 Setting the Window Format

B.8 Plotting Points in a Scattergram

B.9 Tracing a Scattergram

B.10 Graphing Equations with a Scattergram

B.11 Tracing a Curve with a Scattergram

B.12 Turning a Plotter On or Off

B.13 Creating a Table

B.14 Creating a Table for Two Equations

B.15 Using “Ask” in a Table

B.16 Finding the Regression Curve for Some Data

B.17 Plotting Points in Two Scattergrams

B.18 Finding the Intersection Point(s) of Two Curves

B.19 Finding the Minimum Point(s) or Maximum Point(s) of a Curve

B.20 Storing a Value

B.21 Finding Any x-Intercepts of a Curve

B.22 Turning an Equation On or Off

B.23 Finding Coordinates of Points

B.24 Graphing Equations with Axes “Turned Off”

B.25 Entering an Equation by Using *Y*_{n} References

B.26 Responding to Error Messages

Answers to Odd-Numbered Exercises

Index