Course Syllabus: Syllabus
Properties and Attributes of Functions
This unit begins with an introduction to different forms of notation for sets of numbers. Inequality and interval are by far the most used notation, with interval being my favorite because of how much information is given in such a concise format. Features of functions include: maximums, minimums, increasing and decreasing intervals, and domain and range. All of these characteristics provide a stepping off point for the discussion of functions in later units. Additionally, the basics for transformation of functions are addressed here. Transformations are applicable to each type of function that we study and are reviewed as each comes up.
This unit begins with an introduction to different forms of notation for sets of numbers. Inequality and interval are by far the most used notation, with interval being my favorite because of how much information is given in such a concise format. Features of functions include: maximums, minimums, increasing and decreasing intervals, and domain and range. All of these characteristics provide a stepping off point for the discussion of functions in later units. Additionally, the basics for transformation of functions are addressed here. Transformations are applicable to each type of function that we study and are reviewed as each comes up.
8/22 Interval, Set, & Inequality Notation |
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8/23 Function Notation |
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8/24 Transformations in Function Notation |
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8/25 - 8/26 Function Composition |
8/29 Domain and Range |
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8/30 Domain and Range plus End Behavior |
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8/31 Characteristics of Graphs |
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9/1 - 9/2 Parent Functions and Their Attributes |
9/6 Review Properties of Functions |
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9/8 Inverse Relations |
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9/9 Finding and Proving Inverses |
9/12-9/13 Vertex Form of a Quadratic |
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9/14-9/15 Horizontal and Vertical Parabolas |
9/20-9/21 Parabola Application |
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9/23 Regression on the Calculator |
9/26 Parabolic Modeling |
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9/27 Review |
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9/29 Standard Form of a Quadratic |
10/3 Standard to Vertex Form |
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10/4 Completing the Square Day 1 |
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10/5 Completing the Square Day 2 |
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10/6 Solving by Completing the Square |
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10/7 Factoring |
10/11 Factoring to Find Solutions |
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10/12 Writing an Equation from Zeros/Factors |
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10/13-10/14 Quadratic Formula |
10/17 Review Solving Quadratics |
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10/20 Reasonable Domain and Range |
10/24 Quadratic Inequalities |
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10/26-10/27 Linear and Quadratic Systems |
10/31 Angry Birds Project |
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11/3 Solving 2x2 Linear Systems by Graphing & Substitution |
11/7-11/8 Solving 3x3 Systems |
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11/9 3x3 System Application Problems |
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11/10 Solving Linear Inequalities by Graphing |
11/14-11/15 Systems of Inequalities Application (Linear Programming) |
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11/16 Review |
11/28 Matrix Basics |
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11/29 Matrix Multiplication |
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11/30 Determinant of a Matrix |
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12/1 Inverse of a Matrix |
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Extra Credit: Matrix Encryption |
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12/2 Gauss Elimination |
12/7 Matrix Review |
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12/9 Fall Semester Exam Review |
1/3 Properties of Absolute Value Functions |
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1/4 Transformation of Absolute Value Functions |
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1/5 Writing Absolute Value as Piecewise |
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1/6 Writing Absolute Value Equations |
1/11-1/12 Solving Absolute Value Equations |
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1/13 Solving Absolute Value Inequalities |
1/17 Review Absolute Value |
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1/19 Properties of Square Root Functions |
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1/20 Transformation of Square Roots |
1/23-1/24 Solving Square Root Equations |
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1/25 Square Root Applications |
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1/26 Curve Fitting to Square Roots |
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1/27 Curve Fitting to Scatter Plots |
1/30-1/31 Period of a Pendulum Activity |
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2/1 Review for Square Roots |
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2/3 Cubic and Cube Root Functions |
2/6 Cubic and Cube Roots as Inverses |
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2/7 Graphing Cubic and Cube Root Functions |
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2/8 Transformations of Cubic and Cube Root Functions |
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2/9 Effects of Transformations |
2/13 Solving Cubic (and Other Power) Functions |
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2/14 Solving Cube Root (and Other Power) Functions |
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2/15 Cubic/Cube Root Applications |
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2/16 Review |
2/21 Polynomial Basics |
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2/22 Add and Subtract Polynomials |
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2/23 Multiplying Polynomials |
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2/24 Pascal's Triangle |
2/27 Graphing Polynomials |
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2/28 Multiplicity of Roots |
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3/1 Review of Factoring |
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3/2 Factoring by Grouping |
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3/3 Factoring by Sum/Difference of Cubes |
3/6-3/7 Long Division |
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3/8-3/9 Polynomial Operations and Graphing Review |
3/20 Synthetic Division |
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3/21 Solving Polynomials by Factoring |
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3/22-3/23 Solving Polynomials with Complex Roots |
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REVIEW Solving Polynomials |
3/28-3/29 Graphing Rational Functions |
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3/31 Oblique Asymptotes |
4/3-4/4 Multiplying and Dividing Rational Functions |
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4/5 Writing Equations of Rational Functions |
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4/6-4/7 Adding and Subtracting Rational Functions |
4/10 Solving Rational Equations |
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4/11 Solving Rational Inequalities |
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4/13 "Work" Problems and Direct/Inverse Variation |
4/18-4/19 REVIEW Rationals |
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4/21 Exponent Properties |
4/24 Change of Base |
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4/25 Exponential and Logarithmic Properties/Conversion |
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4/26 Properties of Logarithms Expansion |
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4/27 Properties of Logarithms Contraction |
5/1-5/2 Solving Exponential and Log Equations |
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5/3-5/4 Graphing Exponentials and Logs |
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5/5 Exponentials and Logs as Inverses |
5/8 Exponential Growth and Decay |
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5/9 Applications of Logarithms |
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5/10 Compound and Continuous Interest |
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5/11-5/12 Mini-Project Compound Interest |
5/15 Exponential Modeling/Regression |