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0321927338 / 9780321927330 A Graphical Approach to Algebra and Trigonometry
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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.
Table of Contents
1. Linear Functions, Equations, and Inequalities
1.1 Real Numbers and the Rectangular Coordinate System
1.2 Introduction to Relations and Functions
1.3 Linear Functions
1.4 Equations of Lines and Linear Models
1.5 Linear Equations and Inequalities
1.6 Applications of Linear Functions
2. Analysis of Graphs of Functions
2.1 Graphs of Basic Functions and Relations; Symmetry
2.2 Vertical and Horizontal Shifts of Graphs
2.3 Stretching, Shrinking, and Reflecting Graphs
2.4 Absolute Value Functions
2.5 Piecewise-Defined Functions
2.6 Operations and Composition
3. Polynomial Functions
3.1 Complex Numbers
3.2 Quadratic Functions and Graphs
3.3 Quadratic Equations and Inequalities
3.4 Applications of Quadratic Functions and Models
3.5 Higher-Degree Polynomial Functions and Graphs
3.6 Topics in the Theory of Polynomial Functions (I)
3.7 Topics in the Theory of Polynomial Functions (II)
3.8 Polynomial Equations and Inequalities; Further Applications and Models
4. Rational, Power, and Root Functions
4.1 Rational Functions and Graphs I
4.2 Rational Functions and Graphs II
4.3 Rational Equations, Inequalities, Models, and Applications
4.4 Functions Defined by Powers and Roots
4.5 Equations, Inequalities, and Applications Involving Root Functions
5. Inverse, Exponential, and Logarithmic Functions
5.1 Inverse Functions
5.2 Exponential Functions
5.3 Logarithms and Their Properties
5.4 Logarithmic Functions
5.5 Exponential and Logarithmic Equations and Inequalities
5.6 Further Applications and Modeling with Exponential and Logarithmic Functions
6. Systems and Matrices
6.1 Systems of Equations
6.2 Solution of Linear Systems in Three Variables
6.3 Solution of Linear Systems by Row Transformations
6.4 Matrix Properties and Operations
6.5 Determinants and Cramer's Rule
6.6 Solution of Linear Systems by Matrix Inverses
6.7 Systems of Inequalities and Linear Programming
6.8 Partial Fractions
7. Analytic Geometry and Nonlinear Systems
7.1 Circles and Parabolas
7.2 Ellipses and Hyperbolas
7.3 The Conic Sections and Nonlinear Systems
7.4 Parametric Equations
8. Trigonometric Functions and Applications
8.1 Angles and Their Measures
8.2 Trigonometric Functions and Fundamental Identities
8.3 Right Triangles and Evaluating Trigonometric Functions
8.4 Applications of Right Triangles
8.5 The Circular Functions
8.6 Graphs of the Sine and Cosine Functions
8.7 Graphs of the Other Circular Functions
8.8 Harmonic Motion
9. Trigonometric Identities and Equations
9.1 Trigonometric Identities
9.2 Sum and Difference Identities
9.3 Further Identities
9.4 The Inverse Circular Functions
9.5 Trigonometric Equations and Inequalities (I)
9.6 Trigonometric Equations and Inequalities (II)
10. Applications of Trigonometry and Vectors
10.1 The Law of Sines
10.2 The Law of Cosines and Area Formulas
10.3 Vectors and Their Applications
10.4 Trigonometric (Polar) Form of Complex Numbers
10.5 Powers and Roots of Complex Numbers
10.6 Polar Equations and Graphs
10.7 More Parametric Equations
11. Further Topics in Algebra
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 Geometric Sequences and Series
11.4 Counting Theory
11.5 The Binomial Theorem
11.6 Mathematical Induction
R. Reference: Basic Algebraic Concepts
R.1 Review of Exponents and Polynomials
R.2 Review of Factoring
R.3 Review of Rational Expressions
R.4 Review of Negative and Rational ExponentsR.5 Review of Radicals
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