[Book Cover]

Intermediate Algebra: A Journey by Discovery of Curve-Fitting, Preliminary Edition, 1/e

Jay Lehmann, College of San Mateo

Published November, 1997 by Prentice Hall Engineering/Science/Mathematics

Copyright 1998, 675 pp.
Paper
ISBN 0-13-273186-X


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Summary

Unique, enthusiastic approach, this text requires students to take an active role in studying mathematics. Focusing more on the mathematical process, students have abundant opportunities to make intuitive leaps to discover patterns — helping them develop critical thinking skills as well as mathematical confidence. Placing an emphasis on the usefulness of algebra throughout, students discover mathematical concepts while en route to solving true-to-life problems.

Features


Most of the problems presented involve real data collected from scientific experiments and the census and require the use of a graphing calculator.
The use of the graphing utility extends from exploring concepts to verification of conjectures and pattern recognition.
Concepts are introduced graphically, numerically and symbolically.
Hands-on explorations get students to gain a solid understanding of functions, composition of functions, inverse functions using functions to model true-to-life situations and domain and range.
Emphasizes and encourages the process of discovery to come to solutions, reinforcing the concept of active learning.
Text exercises ask students to discuss mathematics and summarize their findings in writing to reinforce conceptual understanding.
Includes collaborative projects that foster teamwork among students.
Math is presented as a powerful tool reinforcing the idea that an understanding of algebra can often put an individual in a position of power to make better conjectures and predictions.


Table of Contents

    1. Using Qualitative Graphs to Describe Situations.

      Using Qualitative Graphs to Describe Situations.

    2. Modeling with Linear Functions.

      Making Predictions: From Tables to Graphs by Hand. Making Predictions: A Graphing Calculator Approach. Going from Equations to Graphs. Computing and Interpreting the Slope of a Line. Finding an Equation. Making Predictions: A Symbolic Approach. Combining Functions to Form New Ones. Finding Inverse Functions. Making More Predictions. Taking It to the Lab.

    3. Modeling with Linear Systems.

      Making Predictions: From Tables to Graphs. Making Predictions: Symbolic Approaches. Making Predictions: From Systems to Inequalities. Taking It to the Lab.

    4. Modeling with Quadratic Functions.

      Making Predictions: From Tables to Graphs. Going from Equations in Vertex Form to Graphs. Going from Equations in Standard Form to Graphs. Finding an Equation. Making Predictions: A Symbolic Approach. Combining Functions to Form New Ones. Taking It to the Lab.

    5. Modeling with Exponential Functions.

      Making Predictions: From Tables to Formulas. Using Exponential Properties. Going From Equations to Graphs. Finding an Equation. Making Predictions: A Symbolic Approach. Combining Functions and Finding Inverse Functions. Making Predictions: Using Properties of Logarithms. Graphing Logarithmic Functions. Taking It to the Lab.

    6. Modeling with Sequences and Series.

      Making Predictions Using Arithmetic Sequences. Making Predictions Using Geometric Sequences. Making Predictions Using Arithmetic Series. Making Predictions Using Geometric Series. Taking It to the Lab.

    7. Modeling with Rational Functions.

      Making Predictions: Using Power Functions. Multiplying and Dividing Rational Functions. Adding and Subtracting Rational Functions. Making Predictions: Using Rational Functions. Taking It to the Lab.

    8. Modeling with Radical Functions.

      Making Predictions: From Tables to Graphs. Going From Equations to Graphs. Making Predictions: A Symbolic Approach. Simplifying Functions and Solving Equations. Taking It to the Lab.

    Appendix A. Using a TI-82 or TI-83 Graphing Calculator.

      Turning Your Graphing Calculator On and Off. Making Your Screen Lighter or Darker. Entering a Function. Graphing a Function. Tracing a Function without a Scattergram. Zooming. Setting the Window Format. Plotting Points for a Scattergram. Tracing a Scattergram without a Function. Graphing Functions with a Scattergram. Tracing a Function with a Scattergram. Turning a Plotter “On” or “Off.” Creating a Table. Creating a Table for Two Functions. Using “Ask” in a Table. Finding the Regression Curve for Some Data. Plotting Points for Two Scattergrams. Finding the Intersection Point(s) of Two Curves. Finding the Minimum or Maximum of a Curve. Graphing Sequences. Turning a Function “On” or “Off.” Using the “Value” Choice. Finding Coordinates of Points. Graphing Functions with Axes “Turned Off.” Entering a Function using Yn references. Responding to Error Messages.

    Appendix B. Comparing TI-82/83/85/86 Calculator Commands.
    Appendix C. Answers to Selected Homework Exercises.
    Index.


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