A Graphical Approach to Algebra and Trigonometry / Edition 5


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Hornsby/Lial/Rockswold’s Graphical Approach covers functions through a consistent four part analytical process that asks students to 1) Examine the nature of the graph 2) Solve a typical equation analytically and graphically 3) Solve the related inequality analytically and graphically, and finally, 4) Apply analytic and graphical methods to solve an application of that class of function.

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Product Details

  • ISBN-13: 9780321764775
  • Publisher: Pearson Education
  • Publication date: 11/23/2012
  • Sold by: Barnes & Noble
  • Format: eTextbook
  • Edition number: 5
  • Pages: 992
  • File size: 143 MB
  • Note: This product may take a few minutes to download.

Meet the Author

John Hornsby: When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics, education, or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, all three of his goals have been realized; his love for teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John’s personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was most recently affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology, and trips to various digs and ruin sites produced fascinating problems for her textbooks, involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

Gary Rockswold has been teaching mathematics for 33 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate, and graduate students, and adult education classes. Now retired, he most recently served as professor of mathematics at Minnesota State University–Mankato. He graduated with majors in mathematics and physics from St. Olaf College in Northfield, Minnesota, where he was elected to Phi Beta Kappa. He received his Ph.D. in applied mathematics from Iowa State University. He has an interdisciplinary background and has also taught physical science, astronomy, and computer science. Outside of mathematics, he enjoys spending time with his lovely wife and two children.

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Table of Contents

(Each chapter (except Chapter R) concludes with a Chapter Summary, Review Exercises, Chapter Test, and Student Project.)
1. Rectangular Coordinates, Functions, and Analysis of Linear Functions.
Real Numbers, Logic, and Coordinate Systems.
Introduction to Relations and Functions.
Linear Functions.
Equations of Lines and Geometric Considerations.
Solution of Linear Equations; Analytic Method and Graphical Support.
Linear Models.
Other Applications of Linear Functions.

2. Analysis of Graphs of Functions.
Graphs of Elementary Functions and Relations.
Vertical and Horizontal Shifts of Graphs of Functions.
Stretching, Shrinking, and Reflecting Graphs of Functions.
The Absolute Value Function: Graphs, Equations, Inequalities, and Applications.
Piecewise Defined Functions Further Topics in the Study of Functions.

3. Polynomial Functions.
Complex Numbers.
Quadratic Functions and Their Graphs.
Solution of Quadratic Equations and Inequalities.
Applications of Quadratic Functions and Models.
Higher Degree Polynomial Functions and Their Graphs.
Topics in the Theory of Polynomial Functions (I).
Topics in the Theory of Polynomial Functions (II).
Solution of Polynomial Equations and Inequalities and Their Applications.

4. Rational and Root Functions; Inverse Functions.
Graphs of Rational Functions.
Rational Equations, Inequalities, and Applications.
Graphs of Root Functions.
Root Equations, Inequalities, and Applications.
Inverse Functions.

5. Exponential and Logarithmic Functions.
Introduction to Exponential Functions.
Logarithms and Their Properties.
Introduction to Logarithmic Functions.
Exponential and Logarithmic Equations and Inequalities.
Applications and Modeling with Exponential and Logarithmic Functions.

6. The Conic Sections and Parametric Equations.
Circles and Parabolas.
Ellipses and Hyperbolas.
Summary of the Conic Sections.
Parametric Equations.

7. Matrices and Systems of Equations and Inequalities.
Systems of Equations.
Solution of Linear Systems by the Echelon Method.
Solution of Linear Systems by Row Transformations.
Properties of Matrices.
Determinants and Cramer's Rule.
Solution of Linear Systems by Matrix Inverses.
Systems of Inequalities and Linear Programming.
Partial Fractions.

8. The Trigonometric Functions and Applications.
Angles and Their Measures.
The Trigonometric Functions and the Fundamental Identities.
Evaluating Trigonometric Functions and the Fundamental Identities.
Evaluating Trigonometric Functions.
Applications of Right Triangle Trigonometry.
The Circular Functions.
Analysis of the Sine and Cosine Functions.
Analysis of Other Circular Functions

9. Trigonometric Identities and Equations.
Identities: Analytic Verification and Graphical Support.
Further Identities.
The Inverse Circular Functions.
Trigonometric Equations and Inequalities.
Further Equations and Inequalities.

11. Applications of Trigonometry: Vectors.
The Law of Sines.
The Law of Cosines and Area Formulas.
Vectors and Their Applications.
Trigonometric (Polar) Form of Complex Numbers.
Powers and Roots of Complex Numbers.
Polar Coordinates and Polar Inequalities.

11. Further Topics in Algebra.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
The Binomial Theorem.
Mathematical Induction.
Counting Theory.

R. Reference: Basic Algebraic Concepts.
Review of Rules for Exponents and Operations with Polynomials.
Review of Factoring.
Review of Operations with Rational Expressions.
Review of Negative and Rational Exponents.
Review of Radicals.

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