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Modeling, Functions, and Graphs
Algebra for College Students
Katherine Yoshiwara
Contents
Index
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Annotations
Contents
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Front Matter
Colophon
Preface
1
Functions and Their Graphs
Linear Models
Functions
Graphs of Functions
Slope and Rate of Change
Linear Functions
Linear Regression
Chapter Summary and Review
Projects for Chapter 1
2
Modeling with Functions
Nonlinear Models
Some Basic Functions
Transformations of Graphs
Functions as Mathematical Models
The Absolute Value Function
Domain and Range
Chapter Summary and Review
Projects for Chapter 2: Periodic Functions
3
Power Functions
Variation
Integer Exponents
Roots and Radicals
Rational Exponents
Joint Variation
Chapter Summary and Review
Projects for Chapter 3
4
Exponential Functions
Exponential Growth and Decay
Exponential Functions
Logarithms
Properties of Logarithms
Exponential Models
Chapter Summary and Review
Projects for Chapter 4
5
Logarithmic Functions
Inverse Functions
Logarithmic Functions
The Natural Base
Logarithmic Scales
Chapter Summary and Review
Projects for Chapter 5
6
Quadratic Functions
Factors and \(x\)-Intercepts
Solving Quadratic Equations
Graphing Parabolas
Problem Solving
Quadratic Inequalities
Curve Fitting
Chapter Summary and Review
Projects for Chapter 6
7
Polynomial and Rational Functions
Polynomial Functions
Graphing Polynomial Functions
Complex Numbers
Graphing Rational Functions
Equations That Include Algebraic Fractions
Chapter Summary and Review
Projects for Chapter 7
8
Linear Systems
Systems of Linear Equations in Two Variables
Systems of Linear Equations in Three Variables
Solving Linear Systems Using Matrices
Linear Inequalities
Linear Programming
Chapter Summary and Review
Projects for Chapter 8
Appendices
A
Algebra Skills Refresher
Numbers and Operations
Linear Equations and Inequalities
Algebraic Expressions and Problem Solving
Graphs and Equations
Linear Systems in Two Variables
Laws of Exponents
Polynomials and Factoring
Factoring Quadratic Trinomials
Working with Algebraic Fractions
Working with Radicals
Facts from Geometry
Properties of Lines
The Real Number System
B
Using a Graphing Calculator
Getting Started
Entering Expressions
Editing Expressions
Graphing an Equation
Making a Table
Regression
Function Notation and Transformation of Graphs
C
Glossary
D
Geometry formulas
E
Answers to Selected Exercises
F
GNU Free Documentation License
Bibliography
Index
Colophon
Authored in PreTeXt
Modeling, Functions, and Graphs
Algebra for College Students
Katherine Yoshiwara
Department of Mathematics
Los Angeles Pierce College
January 27, 2019
Colophon
Preface
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