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Algebra Toolkit
Katherine Yoshiwara
Contents
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Contents
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Front Matter
Colophon
Preface
1
Linear Models
Linear Models
Graphs and Equations
Intercepts
Slope
Equations of Lines
2
Applications of Linear Models
Linear Regression
Linear Systems
Algebraic Solution of Systems
Gaussian Reduction
Linear Inequalities in Two Variables
3
Quadratic Models
Extraction of Roots
Intercepts and Factors
Graphing Parabolas
Completing the Square
4
Applications of Quadratic Models
Quadratic Formula
The Vertex
Curve Fitting
Quadratic Inequalities
5
Functions
Functions
Graphs of Functions
Some Basic Functions
Direct Variation
Inverse Variation
Functions as Mathematical Models
6
Powers and Roots
Integer Exponents
Roots and Radicals
Rational Exponents
Working with Radicals
Radical Equations
7
Exponential Functions
Exponential Growth and Decay
Exponential Functions
Logarithms
Properties of Logarithms
Exponential Models
8
Polynomial and Rational Functions
Polynomial Functions
Algebraic Fractions
Operations on Algebraic Fractions
More Operations on Algebraic Fractions
Equations with Algebraic Fractions
9
Equations and Graphs
Properties of Lines
Distance and Midpoint Formulas
Conic Sections: Ellipses
Conic Sections: Hyperbolas
Nonlinear Systems
10
Logarithmic Functions
Logarithmic Functions
Log Scales
The Natural Base
Authored in PreTeXt
Algebra Toolkit
Katherine Yoshiwara
Department of Mathematics
Los Angeles Pierce College
August 19, 2020
Colophon
Preface