# Elementary and Intermediate Algebra Functions & Authentic Applications

**by**Lehmann, Jay

### 9780321621078

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## Summary

## Author Biography

**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.

I 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).

## Table of Contents

**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*

*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*

*Chapter Summary*

*Key Points of Chapter 2*

*Chapter 2 Review Exercises*

*Chapter 2 Test*

*Cumulative Review of Chapters 1 and 2*

**3. Using the 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 the Slope to Graph Linear Equations

3.5 Rate of Change

*Taking It to the 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*

*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*

*Chapter Summary*

*Key Points of Chapter 6*

*Chapter 6 Review Exercises*

*Chapter 6 Test*

*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

*Taking It to the 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*

*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 Modeling with Exponential Functions

*Taking It to the Lab*

*Chapter Summary*

*Key Points of Chapter 10*

*Chapter 10 Review Exercises*

*Chapter 10 Test*

**11. Logarithmic Functions**

11.1 Inverse Functions

11.2 Logarithmic Functions

11.3 Properties of Logarithms

11.4 Using the Power Property with Exponential Models to Make Predictions

11.5 More Properties of Logarithms

11.6 Natural Logarithms

*Taking It to the Lab*

*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

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*

*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*

*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*

*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

15.2 Performing Operations with Complex Numbers

15.3 Pythagorean Theorem, Distance Formula, and Circles

15.4 Ellipses and Hyperbolas

15.5 Solving Nonlinear Systems of Equations

Appendix A: Using a TI-83/84 Graphing Calculator