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Advanced Functions – Table of Contents Table of Contents Unit 1: Prerequisite Skills 1.1 Slope and Rate of Change .................................................................................. 1 1.2 Cost vs. Time Functions ..................................................................................... 4 1.3 Distance vs. Time Functions ............................................................................... 8 1.4 Common Factoring .......................................................................................... 11 1.5 Factoring Perfect Square Trinomials .................................................................. 12 1.6 Factoring Differences of Squares ...................................................................... 15 1.7 Factoring Trinomials ........................................................................................ 17 1.8 Graphing Systems of Inequalities ...................................................................... 21 Review ................................................................................................................. 25 Unit 2: Functions 2.1 Introduction to Functions ................................................................................. 30 2.2 Function Notation and Evaluation ..................................................................... 31 2.3 Domain of a Function and Interval Notation ...................................................... 34 2.4 Range of a Function and Interval Notation ........................................................ 38 2.5 Adding and Subtracting Functions ..................................................................... 41 2.6 Multiplying and Dividing Functions .................................................................... 44 2.7 Composition of Functions ................................................................................. 48 2.8 Inverse Functions ............................................................................................ 51 2.9 Composition and Inverses ................................................................................ 57 Review ................................................................................................................. 61 ii © Copyright 2020 UnLock Math Inc. Unit 3: Polynomials 3.1 Introduction to Polynomials .............................................................................. 67 3.2 Finding a Polynomial Given the Roots ............................................................... 68 3.3 Dividing Polynomials Using Long Division .......................................................... 72 3.4 Dividing Polynomials Using Synthetic Division .................................................... 74 3.5 Remainder Theorem ........................................................................................ 77 3.6 Factor Theorem .............................................................................................. 79 3.7 Factoring Using Sum or Difference of Cubes ...................................................... 81 Review ................................................................................................................. 84 Unit 4: Polynomials II 4.1 Location Principle and Multiplicity of Zeros ........................................................ 90 4.2 Rational Root Theorem .................................................................................... 94 4.3 Complex Conjugate Root Theorem ................................................................... 99 4.4 Fundamental Theorem of Algebra .................................................................... 103 4.5 Graphing the Cubic Function ........................................................................... 108 4.6 Graphing Polynomials ..................................................................................... 111 4.7 Tangent and Secant Lines ............................................................................... 118 Review ................................................................................................................ 124 Unit 5: Rational Functions 5.1 Introduction to Rational Functions ................................................................... 132 5.2 Simplifying Rational Expressions ...................................................................... 133 5.3 Adding and Subtracting Rational Expressions .................................................... 138 5.4 Multiplying Rational Expressions ...................................................................... 145 iii © Copyright 2020 UnLock Math Inc. 5.5 Dividing Rational Expressions .......................................................................... 149 5.6 Complex Fractions .......................................................................................... 153 5.7 Solving Rational Equations .............................................................................. 155 5.8 Graphing Rational Functions ............................................................................ 160 5.9 Graphing Rational Functions Part II ................................................................. 168 Review ................................................................................................................ 172 Unit 6: Properties of Logarithms 6.1 Introduction to Exponential and Logarithmic Properties ..................................... 179 6.2 Logarithmic Functions ..................................................................................... 182 6.3 Evaluating Logarithmic Functions ..................................................................... 184 6.4 Product Property of Logarithms ....................................................................... 188 6.5 Quotient Property of Logarithms ...................................................................... 192 6.6 Power Property of Logarithms ......................................................................... 196 6.7 The Exponential-Logarithmic Inverse Property .................................................. 200 Review ................................................................................................................ 205 Unit 7: Exponential and Logarithmic Functions 7.1 Graphing Exponential Functions ....................................................................... 212 7.2 Applications of Logarithms .............................................................................. 216 7.3 The Natural Exponential Function .................................................................... 222 7.4 The Natural Logarithm .................................................................................... 225 7.5 Solving Exponential Equations ......................................................................... 229 7.6 Solving Logarithmic Equations ......................................................................... 234 7.7 Exponential and Logarithmic Models ................................................................ 238 Review ................................................................................................................ 242 iv © Copyright 2020 UnLock Math Inc. Unit 8: Trigonometric Functions 8.1 Introduction to Trigonometric Functions ........................................................... 249 8.2 Radian Measure ............................................................................................. 252 8.3 Standard Position and Reference Angles .......................................................... 256 8.4 Special Triangles and Exact Ratios ................................................................... 261 8.5 Graphing the Sine and Cosine Functions ........................................................... 269 8.6 Graphing the Tangent and Cotangent Functions ............................................... 276 8.7 Graphing the Secant and Cosecant Functions ................................................... 280 8.8 Applications of Trigonometric Functions ........................................................... 284 8.9 Modelling Trigonometric Functions ................................................................... 288 8.10 Inverse Trigonometric Functions .................................................................... 294 Review ................................................................................................................ 300 Unit 9: Analytic Trigonometry 9.1 Introduction to Analytic Trigonometry .............................................................. 312 9.2 Cofunction, Periodicity and Negative Angle Identities ........................................ 316 9.3 Addition and Subtraction Identities .................................................................. 323 9.4 Double and Half-Angle Identities ..................................................................... 331 9.5 Product to Sum Identities ............................................................................... 337 9.6 Solving Trigonometric Equations Algebraically ................................................... 342 9.7 Solving Trigonometric Equations with Identities ................................................ 348 Review ................................................................................................................ 352 Glossary ............................................................................................................ 359 v © Copyright 2020 UnLock Math Inc. .
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