Jay Lehmann is passionate about answering the question so many math instructors hear their students ask: But what is this good for? He discovered that a curve fitting approach could enable students to see how math is used in all walks of life with current, compelling, and authentic situations. In addition to curve fitting, Lehmann's approach includes other types of meaningful modeling, directed-discovery explorations, conceptual questions, labs, 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.
Table of Contents:
Note: Each chapter concludes with Chapter Summary, Key Points of the Chapter, Chapter Review Exercises, and Chapter Practice Tests.
Chapter 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 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
Chapter 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
Chapter 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
Chapter 5: Logarithmic Functions
5.1 Inverse Functions
5.2 Logarithmic Functions
5.3 Properties of Logarithms
5.4 Using the Power Property with Exponential Models to Make Predictions
5.5 More Properties of Logarithms
5.6 Natural Logarithms
Chapter 6: Polynomial Functions
6.1 Adding and Subtracting Polynomial Expressions and Functions
6.2 Multiplying Polynomial Expressions and Functions
6.3 Factoring Trinomials of the Form x2 + bx + c; Factoring Out the GCF
6.4 Factoring Polynomials
6.5 Factoring Special Binomials; A Factoring Strategy
6.6 Using Factoring to Solve Polynomial Equations
Chapter 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
Chapter 8: Rational Functions
8.1 Finding the Domains of Rational Functions and Simplifying Rational Expressions
8.2 Multiplying and Dividing Rational Expressions
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
Chapter 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
Chapter 10: Sequences and Series
10.1 Arithmetic Sequences
10.2 Geometric Sequences
10.3 Arithmetic Series
10.4 Geometric Series
Chapter 11: Additional Topics
11.1 Absolute Value: Equations and Inequalities
11.2 Linear Inequalities in Two Variables; Systems of Linear Inequalities
11.3 Performing Operations with Complex Numbers
11.4 Pythagorean Theorem, Distance Formula, and Circles
11.5 Ellipses and Parabolas
11.6 Solving Nonlinear Systems of Equations
Appendix 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
Appendix B: Using a TI-83 or TI-84 Graphing Calculator
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 or Maximum 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 Yn References
B.26 Responding to Error Messages
Answers to Odd-Numbered Exercises
