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Intermediate Algebra: Functions and Authentic Applications, 6th edition

Published by Pearson (February 20, 2018) © 2019

  • Jay Lehmann College of San Mateo

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For courses in Intermediate Algebra.

Looking for a new sound in algebra?

Seeking to answer students' perennial question “But what is this good for?” Intermediate Algebra  models authentic data through curve-fitting to give new meaning to the math. It uses authentic, real-life data sets to find models and derive equations that fit the scenario. The curve-fitting approach teaches the mathematical concepts within the context of data, engaging students from the start and building conceptual understanding. The 6th Edition updates data sets to remain authentic and current, and provides even more resources for students to practice, review and explore the concepts. 

Hallmark features of this title

  • Curve-fitting approach: This central theme guides students through a 4-step modeling process. Students are asked to examine data, find an equation, verify that the model fits the scenario, and use the model to make estimates and predictions.
  • Hundreds of data sets in the text collected from scientific experiments, the Internet, the news and the census teach students to find equations of functions to model the data.
  • Explorations promote active, collaborative learning. Most sections include at least 1 Group Exploration, which are designed to have students apply concepts they have learned in the section in new ways.
  • End-of-section exercise sets include Modeling exercises, Related Review exercises, Expressions, Equations, Functions, and Graphs exercises and more.

New and updated features of this title

  • Updated data sets are as current and relevant as possible:
    • 241 data sets in examples and exercises have been augmented to include recent years.
    • 317 data sets have been replaced with more compelling and timely topics such as immigration, national health care and trust in the mass media.
  • New Large Data Set exercises encompass up to thousands of rows and tens of columns of data and get students comfortable with analyzing big data.
  • New downloadable data sets consist of 16 or more data values and support the appropriate use of technology when completing exercises and labs. These can be downloaded as Excel® files or opened in StatCrunch® for analysis.
  • Updated Taking It To the Lab activities get students hands-on with making their own data and using the scientific method. All 8 Climate Change Labs have been updated to address the latest data and political events concerning this essential global issue.

Features of MyLab Math for the 6th Edition

  • Revised Select exercises with authentic data have been carefully updated to retain their authenticity in MyLab Math, even when regenerating algorithmically. The author has taken special care to ensure that many exercises' algorithmically regenerated versions still ask the student to work with actual data pulled from real-world situations.
  • StatCrunch is available in MyLab Math with this course for the first time. StatCrunch is a web-based statistical software through which students can analyze and share data.
  • Expanded skill, modeling, and conceptual exercises in MyLab Math fully capture the spirit of the print textbook. For the first time, Related Review exercises will be assignable in MyLab Math.
  • The new Concepts and Explorations Notebook: Working with Authentic Data is now available:
    • Gives students opportunities to dig into data and solve problems using pencil and paper
    • Available to download in MyLab Math or printed; includes explorations, modeling exercises, expanded graphing exercises, projects and more.
  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
  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 Lab: Topic of Your Choice
  3. Systems of Linear Equations and Systems of Linear Inequalities
    • 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 (continued from Chapter 2) • Sports Lab • Truck Lab
  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 Your Choice
  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 Logarithm
    • Taking It to the Lab: China and India Populations Lab • Folding Paper Lab • Exponential/Logarithmic Lab: Topic of Your Choice
  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 x2 + 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 (continued from Chapter 3) • Projectile Lab
  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 (continued from Chapter 6) • Projectile Lab (continued from Chapter 6) • Projectile Lab (Using a CBR or CBL) • Water Flow Lab • Quadratic Lab: Topic of Your Choice
  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 (continued from Chapter 7) • Illumination Lab • Boyle’s Law Lab
  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
  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
  11. Additional Topics
    • 11.1 Absolute Value: Equations and Inequalities
    • 11.2 Performing Operations with Complex Numbers
    • 11.3 Pythagorean Theorem, Distance Formula, and Circles
    • 11.4 Ellipses and Hyperbolas
    • 11.5 Solving Nonlinear Systems of Equations

APPENDICES

  • A. Reviewing the Prerequisite Material
  • B. Using a TI-83 or TI- 84 Graphing Calculator
  • C. Using StatCrunch

About our author

Jay Lehmann has taught for the past 25 years at College of San Mateo, where he received the “shiny apple award” for excellence in teaching.  He has presented at over 80 conferences including AMATYC and ICTCM over the past 16 years. Jay is currently the newsletter editor for California Mathematics Council, Community Colleges (CMC3).  Still young at heart, he plays in a rock band appropriately named the Procrastinistas. Jay has authored several algebra textbooks published by Pearson and has also recently completed a Prestatistics textbook.

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 have made it all worthwhile! I'm proud to have played even a small role in raising people's 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).

“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.”

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