Chapter 1: Functions, Graphs, and Models; Linear Functions |
Section | Topic |
1.1 | Functions and Models
1.1.50 Modeling
1.1.64 Modeling
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1.2 | Graphs and Functions
1.2.44 Graphs
1.2.50 Graphs
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1.3 | Linear Functions
1.3.44 Average Rate of Change
1.3.62 Marginal Profit |
1.4 | Equations of Lines
1.4.52 Equation of a Line
1.4.62 Equation of a Line
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Chapter 2: Linear Models, Equations, and Inequalities |
Section | Topic |
2.1 | Algebraic and Graphical Solution of Linear Equations
2.1.68 Solving Algebraically and Graphically
2.1.80 Solve for the Indicated Variable |
2.2 | Fitting Lines to Data Points: Modeling Linear Functions
2.2.34 Line of Best Fit
2.2.44 Line of Best Fit |
2.3 | Systems of Linear Equations in Two Variables
2.3.44 Solve a System in Two Variables
2.3.58 Solve a System in Two Variables |
2.4 | Solution of Linear Inequalities
2.4.38 Solve a Linear Inequality
2.4.52 Solve a Linear Inequality |
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Chapter 3: Quadratic, Piecewise-Defined, and Power Functions |
Section | Topic |
3.1 | Quadratic Functions, Parabolas
3.1.52 Vertex Formula
3.1.72 Vertex Formula |
3.2 | Solving Quadratic Equations
3.2.66 Solving Quadratic Equations
3.2.74 Solving Quadratic Equations |
3.3 | Piecewise-Defined Functions and Power Functions
3.3.48 Piecewise-Defined Function
3.3.52 Power Function |
3.4 | Quadratic and Power Models |
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Chapter 4: Additional Topics with Functions |
Section | Topic |
4.1 | Transformations of Graphs and Symmetry
4.1.64 Transforming Graphs
4.1.70 Transforming Graphs |
4.2 | Combining Functions; Composite Functions
4.2.30 Combining Functions
4.2.48 Composite Functions |
4.3 | One-to-One and Inverse Functions
4.3.32 Inverse Functions
4.3.44 One-to-One and Inverse Functions |
4.4 | Additional Equations and Inequalities
4.4.50 Quadratic Inequality
4.4.60 Quadratic Inequality |
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Chapter 5: Exponential and Logarithmic Functions |
Section | Topic |
5.1 | Exponential Functions
5.1.50 Exponential Function
5.1.54 Exponential Function |
5.2 | Logarithmic Functions; Properties of Logarithms
5.2.44 Logarithmic Function
5.2.48 Logarithmic Function |
5.3 | Exponential and Logarithmic Functions
5.3.52 Doubling Time
5.3.74 Change-of-Base Formula |
5.4 | Exponential and Logarithmic Functions
5.4.20 Exponential Model
5.4.32 Exponential Regression |
5.5 | Exponential Functions and Investing
5.5.30 Time to Double
5.5.42 Future Value |
5.6 | Annuities; Loan Repayment |
5.7 | Logistic and Gompertz Functions |
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Chapter 6: Higher-Degree Polynomial and Rational Functions |
Section | Topic |
6.1 | Higher-Degree Polynomial Functions
6.1.40 Cubic Functions
6.1.46 Local Extrema |
6.2 | Modeling with Cubic and Quartic Functions |
6.3 | Solution of Polynomial Equations
6.3.34 Factoring and the Root Method
6.3.42 Factoring and Grouping |
6.4 | Polynomial Equations and Continued; Fundamental Theorem of Algebra
6.4.34 Synthetic Division
6.4.36 Synthetic Division |
6.5 | Rational Functions and Rational Equations
6.5.38 Rational Functions
6.5.52 Rational Functions |
6.6 | Polynomial and Rational Inequalities |
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Chapter 7: Systems of Equations and Matrices |
Section | Topic |
7.1 | Systems of Linear Equations in Three Variables
7.1.22 Solving Systems in Three Variables
7.1.32 Solving Systems in Three Variables |
7.2 | Matrix Solution of Systems of Linear Equations |
7.3 | Matrix Operations |
7.4 | Inverse Matrices; Matrix Equations |
7.5 | Determinants and Cramer's Rule |
7.6 | Systems of Nonlinear Equations
7.6.30 Systems of Nonlinear Equations
7.6.36 Systems of Nonlinear Equations |
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Chapter 8: Special Topics in Algebra |
Section | Topic |
8.1 | Systems of Inequalities |
8.2 | Linear Programming: Graphical Methods |
8.3 | Sequences and Discrete Functions
8.3.8 Sequences
8.3.14 Sequences |
8.4 | Series
8.4.10 Series
8.4.16 Series |
8.5 | Preparing for Calculus |
8.6 | The Binomial Theorem |
8.7 | Conic Sections: Circles and Parabolas |
8.8 | Conic Sections: Ellipses and Hyperbolas |
