About the Book
This intermediate algebra text, based on standards in the AMATYCCrossroads document, motivates college math students to develop mathematical literacy and a solid foundation for future study in mathematics and other disciplines. This second book of a two-book series presents mathematical concepts and skills through relevant activities derived from real-life situations; these activities are meaningful to students because they illustrate how mathematics arises naturally from real-world situations and problems. Mathematics in Action is based on the assumption that students learn mathematics best by deriving concepts themselves in a meaningful context. The text takes a collaborative approach to learning. Students take an active role in their own learning by working in groups, thereby developing communication skills, a sense of independence, and a “can-do” attitude about mathematics. Technology is integrated throughout the book so that students can learn to interpret real-life data numerically, symbolically, and graphically. Regardless of their level of preparation for the course, students can use this text to increase their knowledge of mathematics, their problem-solving skills, and their overall confidence in their ability to learn.
Table of Contents:
(All clusters include “What Have I Learned?” and “How Can I Practice exercises?”, and each chapter concludes with a “Gateway Review.”)CHAPTER 1. FUNCTION SENSE.
Cluster 1. Modeling with Functions.
Parking Problems.
Function Notation, Graphical and Numerical Representations of a Function.
Fill' er Up.
Function Notation, Symbolic Representation, Domain and Range.
Skid Marks.
Modeling Data with Functions.
Graphs Tell Stories.
Interpreting Graphs of Functions.
Cluster 2. Linear Functions.
Walking for Fitness.
Rate of Change.
Car Speed.
Linear Functions and Slope, Slope-Intercept Form.
A Visit to the Architect.
Determining Linear Models from Two Data Points.
Skateboard Heaven.
General Form of Linear Equations.
College Tuition.
Modeling a Line of Best Fit with a Straightedge, Goodness of Fit, Interpolation and Extrapolation.
Reading a Movie.
Linear Regression.
Cluster 3. Systems of Linear Equations and Absolute Value Functions.
Car Speed Revisited.
2 x 2 Linear Systems—Solving Graphically, Numerically, and Algebraically.
Sam's Café.
Solving 3 x 3 Linear Systems of Equations.
Long Distance By Phone.
Piecewise Linear Functions.
How Much Can You Tolerate?
Absolute Value Function, Inequalities.
Cluster 4. Probability Functions and Statistical Reasoning.
The Class Survey.
Organizing Data, Frequency Distributions, Measures of Central Tendency.
Chances Are!
Relative Frequency, Probability Functions, Simulation.
Choices.
Multiplication Principle of Counting, Tree Diagrams, Sample Space.
A Switch Decision.
Measuring Variability of a Distribution.
CHAPTER 2. THE ALGEBRA OF FUNCTIONS.
Cluster 1. Addition, Subtraction, and Multiplication of Functions.
Spending and Earning Money.
Addition, Subtraction, and Constant Multiples of Functions.
Viewing the Algebra of Functions.
Adding and Subtracting Functions Graphically.
How Does Your Garden Grow?
Product of Functions, Multiplication of Polynomials.
Cluster 2. Composition and Inverse of Functions.
Inflated Balloons.
Composition of Functions.
Finding a Bargain.
Composition of Functions.
The Square of a Cube.
Properties of Exponents, Fractional Exponents.
Study Time.
Introduction to Inverse Functions.
Temperature Conversions.
Determining Inverse Functions, Graphs of Inverse Functions.
Error Checking.
Composition of Functions.
CHAPTER 3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Cluster 1. Exponential Functions.
The Summer Job.
Exponential Functions.
Investment Clubs.
Exponential Functions of the Form y = abx , Recognizing Exponential Functions.
Population Growth.
Exponential Functions of the Form y = a(1+r)t, Growth Rate vs. Growth Factor.
Photocopying Machines.
Exponential Functions, Growth Factor, Decay Factor, Doubling and Halving Time.
Compound Interest.
Exponential Growth, Continuous Growth Rate, Natural Base e.
College Graduates.
Fitting Data to an Exponential Model, Regression Equations.
Cluster 2. Logarithmic Functions.
The Foolish King.
Logarithmic Functions.
The National Pastime.
Graphs of Logarithmic Functions, Modeling Data.
The Elastic Ball.
Properties of Logarithms.
The Coroner's Office.
The Power Property of Logarithmic Functions, Change of Base Formula.
Prison Growth.
Exponential Growth, Solving Exponential Equations.
Frequency and Pitch.
Solving Logarithmic Equations.
CHAPTER 4. QUADRATIC AND HIGHER ORDER POLYNOMIAL FUNCTIONS.
Cluster 1. Introduction to Quadratic Functions.
Baseball Throughout the Solar System.
Introduction to Quadratic Functions and Their Graphs.
Galileo and the Quadratic Function.
The Roles of a, b, and c in y = ax2 + bx + c.
The Shot Put.
Modeling Using the Quadratic Function, Special Features of Parabolas, the Vertex.
Cluster 2. Problem Solving Using Quadratic Functions.
Personal Computers.
Solving Quadratic Equations Graphically and Numerically.
Sir Isaac Newton XIV.
Solving Quadratic Equations by Factoring, The Quadratic Formula.
Complex Numbers.
Introduction to Complex Numbers.
Airfare.
Building a Quadratic Model as a Product of Linear Models, Analyzing a Model Contextually.
Chemical Waste Holding Region.
Problem Solving Using Quadratic Functions.
Cluster 3. Curving Fitting and Higher Order Polynomial Functions.
The Population of Cleveland.
Curve Fitting.
The Power of Power Functions.
Power Functions, Combinations of Power Functions.
Hot Air Balloons.
Polynomial Functions and Their Graphs.
Stolen Bases.
Curve Fitting, General Properties of Cubics and Quartics.
Finding the Maximum Value.
Problem Solving Using Polynomial Functions.
CHAPTER 5. RATIONAL AND RADICAL FUNCTIONS.
Cluster 1. Rational Functions.
Speed Limits.
Properties of Graphs of the form y = k/x.
Loudness of Sound.
Functions of the form f(x) = k/xn.
Percent Markup.
Rational Functions of the form f(x) = k/ax+b.
Blood-Alcohol Levels.
Solving Equations Involving Rational Expressions, Horizontal Asymptotes.
Cluster 2. Radical Functions and Equations.
Hang Time.
Radical Functions, Roots, Fractional Exponents.
Falling Objects.
Radical Equations.
Take a Hike.
Cube Root Functions, nth Roots, Fractional Exponents.
CHAPTER 6. INTRODUCTION TO THE TRIGONOMETRIC FUNCTIONS.
Cluster 1. Introducing the Sine, Cosine, and Tangent Functions.
The Leaning Tower of Pisa.
An Introduction to Right Triangle Trigonometry.
A Gasoline Problem.
Cofunctions and Complementary Angles.
The Sidewalks of New York.
Inverse Trigonometric Functions.
Solving a Murder.
Solving Right Triangles.
How Stable is That Tower?
Problem Solving with Right Triangle Trigonometry.
Climbing a Mountain.
Right Triangle Trigonometry, Algebraic Equation Solving, Problem-Solving Heuristics.
Seeing Abraham Lincoln.
Right Triangle Trigonometry, Inverses of Trigonometric Functions, Geometric Drawing, Optimization by Analyzing Graphs and/or Tables.
Cluster 2. Why are the Trigonometric Functions Called Circular?
Learn Trig or Crash!
Sine and Cosine as Circular Functions.
It Won't Hertz.
Periodic Behavior, Radian Measure.
Get In Shape.
The Amplitude of y = asin(bx + c) and y = acos(bx + c).
Speeding Up.
The Period of y = asin(bx + c) and y = acos(bx + c).
Running With a Friend.
The Displacement of y = asin(bx + c) and y = acos(bx + c).
Appendix A: Concept Review.
Appendix B: Trigonometry.
Appendix C: The TI-83 Graphing Calculator.
Selected Answers.
Glossary.
Index.
