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This text bridges the gap between traditional and reform approaches to algebra encouraging students to see mathematics in context. It presents fewer topics in greater depth, prioritizing data analysis as a foundation for mathematical modeling, and emphasizing the verbal, numerical, graphical and symbolic representations of mathematical concepts as well as connecting mathematics to real life situations drawn from the students' majors.
- The problems, the models and the real life data are the three features of this book. They are used to relate the mathematics to the students' lives and to show the usefulness and relevance of the mathematics to the modern reality.
Making Sense of Data. Visualizing Relationships in Data. Equations: Describing Relationships in Data. Functions: Describing Change. Function Notation: The Concept of Function as a Rule. Working with Functions: Graphs and Graphing Calculators. Working with Functions: Getting Information from the Graph. Working with Functions: Modeling Real-World Relationships. Making and Using Formulas. Concept Check and Review. EXPLORATION 1: Bias in Presenting Data. EXPLORATION 2: Collecting and Analyzing Data. EXPLORATION 3: Every Graph Tells a Story.
2. LINEAR FUNCTIONS AND MODELS.
Working with Functions: Average Rate of Change. Linear Functions: Constant Rate of Change. Equations of Lines: Making Linear Models. Varying the Coefficients: Direct Proportionality. Linear Regression: Fitting Lines to Data. Linear Equations: Getting Information from a Model. Linear Equations: Where Lines Meet. Concept Check and Review. EXPLORATION 1: When Rates of Change. EXPLORATION 2: Linear Patterns. EXPLORATION 3: Bridge Science. EXPLORATION 4: Correlation and Causation. EXPLORATION 5: Fair Division of Assets.
3. EXPONENTIAL FUNCTIONS AND MODELS.
Exponential Growth and Decay. Exponential Models: Comparing Rates. Comparing Linear and Exponential Growth. Graphs of Exponential Functions. Fitting Exponential Curves to Data. Concept Check and Review. EXPLORATION 1: Extreme Numbers: Scientific Notation. EXPLORATION 2: So You Want to be a Millionaire? EXPLORATION 3: Linear Patterns. EXPLORATION 4: Modeling Radioactivity with Coins and Dice.
4. LOGARITHMS AND EXPONENTIAL MODELS.
Logarithmic Functions. Laws of Logarithms. Logarithmic Scales. The Natural Exponential and Logarithmic Functions. Exponential Equations: Getting Information from Model. Working With Functions: Composition and Inverse. Concept Check and Review. EXPLORATION 1: Super Origami. EXPLORATION 2: Orders of Magnitude. EXPLORATION 3: Semi-Log Graphs. EXPLORATION 4: The Even-Tempered Clavier.
5. QUADRATIC FUNCTIONS AND MODELS.
Working with Functions: Shifting and Stretching. Quadratic Functions and their Graphs. Maxima and Minima: Getting Information from a Model. Quadratic Equations: Getting Information from a Model. Fitting Quadratic Curves to Data. Concept Check and Review. EXPLORATION 1: Transformation Stories. EXPLORATION 2: Toricelli''s Law. EXPLORATION 2: Quadratic Patterns.
6. POWER, POLYNOMIAL, AND RATIONAL FUNCTIONS.
Working with Functions: Algebraic Operations. Power Functions: Positive Powers. Polynomial Functions: Combining Power Functions. Fitting Power and Polynomial Curves to Data. Power Functions: Negative Powers. Rational Functions. Concept Check and Review. EXPLORATION 1: Only in the Movies? EXPLORATION 2: Proportionality: Shape and Size. EXPLORATION 3: Managing Traffic. EXPLORATION 4: Alcohol and the Surge Function.
7. SYSTEMS OF EQUATIONS AND CATEGORICAL DATA.
Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. Using Matrices to Solve Systems of Linear Equations. Matrices and Categorical Data. Matrix Operations: Getting Information from Data. Matrix Equations: Solving a Linear System. Concept Check and Review. EXPLORATION 1: Collecting Categorical Data. EXPLORATION 2: Will the Species Survive?
ALGEBRA TOOLKIT A: WORKING WITH NUMBERS.
Numbers and Their Properties. The Number Line and Intervals. Integer Exponents. Radicals and Rational Exponents.
ALGEBRA TOOLKIT B: WORKING WITH EXPRESSIONS.
Combining Algebraic Expressions. Factoring Algebraic Expressions. Rational Expressions.
ALGEBRA TOOLKIT C: WORKING WITH EQUATIONS.
Solving Basic Equations. Solving Quadratic Equations. Solving Basic Inequalities.
ALGEBRA TOOLKIT D: WORKING WITH GRAPHS.
The Coordinate Plane. Graphs of Two-Variable Equations. Using a Graphing Calculator. Solving Equations and Inequalities Graphically.
“I’m excited. I want to do all of the explorations now. When can I get my copy to teach with?”
“It’s a college algebra text that is built on real life examples and concepts. Students learn through using real data, hands on activities, and sections that slowly guide them to extensions of the previous concept. The explorations are wonderful.”
“[This book] gets the students to think beyond the manipulations and see that the mathematics they are learning really does have a purpose.”
“…These are exactly the type of examples that I look for when I review college algebra books for adoption! The applications included are also similar to problems discussed in prominent research articles in mathematics education…”
“Very promising. I like how the exercises are categorized (Fundamentals, Think About It, Skills, Contexts). I also like how material is not used and then forgotten but is used in upcoming sections…”
“It seems a great book; maintaining a good balance of skills-based exercises and explorations-based exercises. I also like the tone of the textbook (story telling) and the connection to real-life applications.”
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
eBank Test Bank
The Test Bank includes every problem that comes loaded in ExamView in an easy to customize text format.
Complete Solutions Manual
This manual contains solutions to all exercises from the text, including Chapter Review Exercises, Chapter Tests, and Cumulative Review Exercises.
This is an electronic version of the complete solutions manual available via the PowerLecture and Instructor's Companion Website. It provides instructors with an efficient method for creating solution sets to homework or exams that can then be printed or posted.
Reinforces student understanding with detailed explanations, worked-out examples, and practice problems. Lists key ideas to master and builds problem-solving skills. There is a section in the Study Guide corresponding to each section in the text.