## Description

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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0321922727 / 9780321922724 Elementary & Intermediate Algebra: Functions and Authentic Applications

## Table of Contents

Preface

Acknowledgments

Index of Applications

**1. Introduction To Modeling**

1.1 Variables And Constants

1.2 Scattergrams

1.3 Exact Linear Relationships

1.4 Approximate Linear Relationships

Taking It To The Lab: Climate Change Lab * Volume Lab * Linear

Graphing Lab: Topic Of Your Choice

Chapter Summary

Key Points Of Chapter 1

Chapter 1 Review Exercises

Chapter 1 Test

**2. Operations And Expressions**

2.1 Expressions

2.2 Operations With Fractions

2.3 Adding Real Numbers

2.4 Change In A Quantity And Subtracting Real Numbers

2.5 Ratios, Percents, And Multiplying And Dividing Real Numbers

2.6 Exponents And Order Of Operations

Taking It To The Lab: Climate Change Lab * Stocks Lab

Chapter Summary

Key Points Of Chapter 2

Chapter 2 Review Exercises

Chapter 2 Test

Cumulative Review Of Chapters 1 And 2

**3. Using Slope To Graph Linear Equations**

3.1 Graphing Equations Of The Form *y = mx + b*

3.2 Graphing Linear Models; Unit Analysis

3.3 Slope Of A Line

3.4 Using Slope To Graph Linear Equations

3.5 Rate Of Change

Taking It To The Lab: Climate Change Lab * Workout

Lab * Balloon Lab

Chapter Summary

Key Points Of Chapter 3

Chapter 3 Review Exercises

Chapter 3 Test

**4. Simplifying Expressions And Solving Equations**

4.1 Commutative, Associative, And Distributive Laws

4.2 Simplifying Expressions

4.3 Solving Linear Equations In One Variable

4.4 Solving More Linear Equations In One Variable

4.5 Comparing Expressions And Equations

4.6 Formulas

Chapter Summary

Key Points Of Chapter 4

Chapter 4 Review Exercises

Chapter 4 Test

Cumulative Review Of Chapters 1—4

**5. Linear Functions And Linear Inequalities In One Variable**

5.1 Graphing Linear Equations

5.2 Functions

5.3 Function Notation

5.4 Finding Linear Equations

5.5 Finding Equations Of Linear Models

5.6 Using Function Notation With Linear Models To Make Estimates And Predictions

5.7 Solving Linear Inequalities In One Variable

Taking It To The Lab: Climate Change Lab * Golf Ball Lab *

Rope Lab * Shadow Lab * Linear Lab: Topic Of Your Choice

Chapter Summary

Key Points Of Chapter 5

Chapter 5 Review Exercises

Chapter 5 Test

**6. Systems Of Linear Equations And Systems Of Linear Inequalities**

6.1 Using Graphs And Tables To Solve Systems

6.2 Using Substitution To Solve Systems

6.3 Using Elimination To Solve Systems

6.4 Using Systems To Model Data

6.5 Perimeter, Value, Interest, And Mixture Problems

6.6 Linear Inequalities In Two Variables; Systems Of Linear

Inequalities In Two Variables

Taking It To The Lab: Climate Change Lab * Sports Lab *

Truck Lab

Chapter Summary

Key Points Of Chapter 6

Chapter 6 Review Exercises

Chapter 6 test 383

Cumulative Review of Chapters 1—6

**7. Polynomial Functions And Properties Of Exponents**

7.1 Adding And Subtracting Polynomial Expressions And Functions

7.2 Multiplying Polynomial Expressions And Functions

7.3 Powers Of Polynomials; Product Of Binomial Conjugates

7.4 Properties Of Exponents

7.5 Dividing Polynomials: Long Division And Synthetic Division

Taking It To The Lab: Climate Change Lab * Projectile Lab

Chapter Summary

Key Points Of Chapter 7

Chapter 7 Review Exercises

Chapter 7 Test

Making Sure You’re Ready For Intermediate Algebra:

A Review Of Chapters 1—7

**8. Factoring Polynomials And Solving Polynomial Equations**

8.1 Factoring Trinomials Of The Form *x ^{2} + bx + c* And Differences of Two Squares

8.2 Factoring Out The GCF; Factoring By Grouping

8.3 Factoring Trinomials Of The Form *ax*^{2} + *bx* + *c*

8.4 Sums And Differences Of Cubes; A Factoring Strategy

8.5 Using Factoring To Solve Polynomial Equations

8.6 Using Factoring To Make Predictions With Quadratic Models

Chapter Summary

Key Points Of Chapter 8

Chapter 8 Review Exercises

Chapter 8 Test

Making Sure You’re Ready For Intermediate Algebra:

A Review Of Chapters 1—8

**9. Quadratic Functions**

9.1 Graphing Quadratic Functions In Vertex Form

9.2 Graphing Quadratic Functions In Standard Form

9.3 Simplifying Radical Expressions

9.4 Using The Square Root Property To Solve Quadratic Equations

9.5 Solving Quadratic Equations By Completing The Square

9.6 Using The Quadratic Formula To Solve Quadratic Equations

9.7 Solving Systems Of Linear Equations In Three Variables; Finding Quadratic Functions

9.8 Finding Quadratic Models

9.9 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 9

Chapter 9 Review Exercises

Chapter 9 Test

Cumulative Review Of Chapters 1—9

**10. Exponential Functions**

10.1 Integer Exponents

10.2 Rational Exponents

10.3 Graphing Exponential Functions

10.4 Finding Equations Of Exponential Functions

10.5 Using Exponential Functions To Model Data

Taking It To The Lab: Stringed Instrument Lab * Cooling Water

Lab * Exponential Lab: Topic Of Your Choice

Chapter Summary

Key Points Of Chapter 10

Chapter 10 Review Exercises

Chapter 10 Test

**11. Logarithmic Functions**

11.1 Composite Functions

11.2 Inverse Functions

11.3 Logarithmic Functions

11.4 Properties Of Logarithms

11.5 Using The Power Property With Exponential Models To Make Predictions

11.6 More Properties Of Logarithms

11.7 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 11

Chapter 11 Review Exercises

Chapter 11 Test

Cumulative Review Of Chapters 1—11

**12. Rational Functions**

12.1 Finding The Domains Of Rational Functions And Simplifying Rational Expressions

12.2 Multiplying And Dividing Rational Expressions; Converting Units

12.3 Adding And Subtracting Rational Expressions

12.4 Simplifying Complex Rational Expressions

12.5 Solving Rational Equations

12.6 Modeling With Rational Functions

12.7 Proportions; Similar Triangles

12.8 Variation

Taking It To The Lab: Climate Change Lab * Illumination

Lab * Boyle’s Law Lab * Estimating P Lab

Chapter Summary

Key Points Of Chapter 12

Chapter 12 Review Exercises

Chapter 12 Test

**13. Radical Functions**

13.1 Simplifying Radical Expressions

13.2 Adding, Subtracting, And Multiplying Radical Expressions

13.3 Rationalizing Denominators And Simplifying Quotients Of Radical Expressions

13.4 Graphing And Combining Square Root Functions

13.5 Solving Radical Equations

13.6 Modeling With Square Root Functions

Taking It To The Lab: Pendulum Lab

Chapter Summary

Key Points Of Chapter 13

Chapter 13 Review Exercises

Chapter 13 Test

**14. Sequences And Series**

14.1 Arithmetic Sequences

14.2 Geometric Sequences

14.3 Arithmetic Series

14.4 Geometric Series

Taking It To The Lab: Bouncing Ball Lab * Stacked Cups Lab

Chapter Summary

Key Points Of Chapter 14

Chapter 14 Review Exercises

Chapter 14 Test

Cumulative Review Of Chapters 1—14

**15. Additional Topics**

15.1 Absolute Value: Equations And Inequalities

Key Points Of Section 15.1

15.2 Performing Operations With Complex Numbers

Key Points Of Section 15.2

15.3 Pythagorean Theorem, Distance Formula, And Circles

Key Points Of Section 15.3

15.4 Ellipses And Hyperbolas

Key Points Of Section 15.4

15.5 Solving Nonlinear Systems Of Equations

Key Points Of Section 15.5

**A. Using A TI-83 Or TI-84 Graphing Calculator (Available Online Only)**

A.1 Turning A Graphing Calculator On Or Off

A.2 Making The Screen Lighter Or Darker

A.3 Entering An Equation

A.4 Graphing An Equation

A.5 Tracing A Curve Without A Scattergram

A.6 Zooming

A.7 Setting The Window Format

A.8 Plotting Points In A Scattergram

A.9 Tracing A Scattergram

A.10 Graphing Equations With A Scattergram

A.11 Tracing A Curve With A Scattergram

A.12 Turning A Plotter On Or Off

A.13 Creating A Table

A.14 Creating A Table For Two Equations

A.15 Using “Ask” In A Table

A.16 Finding The Regression Curve For Some Data

A.17 Plotting Points In Two Scattergrams

A.18 Finding The Intersection Point(S) Of Two Curves

A.19 Finding The Minimum Point(S) Or Maximum Point(S) Of A Curve

A.20 Storing A Value

A.21 Finding Any X-Intercepts Of A Curve

A.22 Turning An Equation On Or Off

A.23 Finding Coordinates Of Points

A.24 Graphing Equations With Axes “Turned Off”

A.25 Entering An Equation By Using *Y _{n}* References

A.26 Responding To Error Messages

Answers To Odd-Numbered Exercises

Index

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