0 Review: Equations and Inequalities 1 0.1 Linear Equations 2 0.1.1 Solving Linear Equations in One Variable 2 0.1.2 Applications Involving Linear Equations 6 0.1.3 Interest Problems 8 0.

1.4 Mixture Problems 10 0.1.5 Distance-Rate-Time Problems 12 0.2 Quadratic Equations 17 0.2.1 Factoring 17 0.2.

2 Square Root Method 19 0.2.3 Completing the Square 21 0.2.4 Quadratic Formula 23 0.2.5 Applications Involving Quadratic Equations 26 0.3 Other Types of Equations 30 0.

3.1 Rational Equations 30 0.3.2 Radical Equations 33 0.3.3 Equations Quadratic in Form: u-Substitution 35 0.3.4 Factorable Equations 37 0.

3.5 Equations Involving Absolute Value 38 0.4 Inequalities 43 0.4.1 Graphing Inequalities and Interval Notation 43 0.4.2 Linear Inequalities 46 0.4.

3 Polynomial Inequalities 48 0.4.4 Rational Inequalities 51 0.4.5 Absolute Value Inequalities 53 0.5 Graphing Equations 58 0.5.1 Cartesian Plane 59 0.

5.2 The Distance and Midpoint Formulas 59 0.5.3 Point-Plotting 61 0.5.4 Using Intercepts as Graphing Aids 62 0.5.5 Using Symmetry as a Graphing Aid 64 0.

5.6 Circles 67 0.6 Lines 74 0.6.1 General Form of a Line and Slope 74 0.6.2 Equations of Lines 77 0.6.

3 Parallel and Perpendicular Lines 80 0.7 Modeling Variation 86 0.7.1 Direct Variation 86 0.7.2 Inverse Variation 88 0.7.3 Joint Variation and Combined Variation 90 0.

8* Linear Regression: Best Fit 0.8-1 0.8.1 Scatterplots 0.8-1 0.8.2 Identifying Patterns 0.8-5 0.

8.3 Linear Regression 0.8-12 Review 95 Review Exercises 97 Practice Test 99 1 Functions and Their Graphs 100 1.1 Functions 101 1.1.1 Relations and Functions 101 1.1.2 Functions Defined by Equations 104 1.

1.3 Function Notation 106 1.1.4 Domain of a Function 110 1.2 Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change 118 1.2.1 Recognizing and Classifying Functions 118 1.2.

2 Increasing and Decreasing Functions 122 1.2.3 Average Rate of Change 125 1.2.4 Piecewise-Defined Functions 128 1.3 Graphing Techniques: Transformations 138 1.3.1 Horizontal and Vertical Shifts 138 1.

3.2 Reflection About the Axes 143 1.3.3 Stretching and Compressing 146 1.4 Operations on Functions and Composition of Functions 152 1.4.1 Adding, Subtracting, Multiplying, and Dividing Functions 153 1.4.

2 Composition of Functions 154 1.5 One-to-One Functions and Inverse Functions 163 1.5.1 Determine Whether a Function Is One-to-One 163 1.5.2 Inverse Functions 166 1.5.3 Graphical Interpretation of Inverse Functions 168 1.

5.4 Finding the Inverse Function 170 Review 179 Review Exercises 181 Practice Test 184 2 Polynomial and Rational Functions 185 2.1 Quadratic Functions 186 2.1.1 Graphs of Quadratic Functions: Parabolas 186 2.1.2 Finding the Equation of a Parabola 195 2.2 Polynomial Functions of Higher Degree 203 2.

2.1 Identifying Polynomial Functions 203 2.2.2 Graphing Polynomial Functions Using Transformations of Power Functions 206 2.2.3 Real Zeros of a Polynomial Function 207 2.2.4 Graphing General Polynomial Functions 210 2.

3 Dividing Polynomials: Long Division and Synthetic Division 219 2.3.1 Long Division of Polynomials 219 2.3.2 Synthetic Division of Polynomials 223 2.4 The Real Zeros of a Polynomial Function 227 2.4.1 The Remainder Theorem and the Factor Theorem 227 2.

4.2 The Rational Zero Theorem and Descartes'' Rule of Signs 230 2.4.3 Factoring Polynomials 234 2.4.4 The Intermediate Value Theorem 236 2.4.5 Graphing Polynomial Functions 238 2 .

5 Complex Zeros: The Fundamental Theorem of Algebra 242 2.5.1 Complex Zeros 243 2.5.2 Factoring Polynomials 247 2.6 Rational Functions 251 2.6.1 Domain of Rational Functions 251 2.

6.2 Vertical, Horizontal, and Slant Asymptotes 253 2.6.3 Graphing Rational Functions 259 Review 271 Review Exercises 273 Practice Test 276 Cumulative Test 277 3 Exponential and Logarithmic Functions 278 3.1 Exponential Functions and Their Graphs 279 3.1.1 Evaluating Exponential Functions 279 3.1.

2 Graphs of Exponential Functions 281 3.1.3 The Natural Base e 285 3.1.4 Applications of Exponential Functions 287 3.2 Logarithmic Functions and Their Graphs 295 3.2.1 Evaluating Logarithms 295 3.

2.2 Common and Natural Logarithms 298 3.2.3 Graphs of Logarithmic Functions 298 3.2.4 Applications of Logarithms 303 3.3 Properties of Logarithms 311 3.3.

1 Properties of Logarithmic Functions 311 3.3.2 Change-of- Base Formula 316 3.4 Exponential and Logarithmic Equations 320 3.4.1 Exponential Equations 320 3.4.2 Solving Logarithmic Equations 324 3.

4.3 Applications 326 3.5 Exponential and Logarithmic Models 331 3.5.1 Exponential Growth Models 332 3.5.2 Exponential Decay Models 333 3.5.

3 Gaussian (Normal) Distribution Models 335 3.5.4 Logistic Growth Models 336 3.5.5 Logarithmic Models 337 Review 343 Review Exercises 345 Practice Test 348 Cumulative Test 349 4 Trigonometric Functions of Angles 350 4.1 Angle Measure 351 4.1.1 Angles and their Measure 352 4.

1.2 Radian Measure 354 4.1.3 Angles in Standard Position 357 4.1.4 Coterminal Angles 358 4.1.5 Arc Length 359 4.

1.6 Area of a Circular Sector 360 4.1.7 Linear and Angular Speed 361 4.1.8 Relationship Between Linear and Angular Speeds 363 4.2 Right Triangle Trigonometry 369 4.2.

1 Right Triangle Ratios 370 4.2.2 Trigonometric Functions: Right Triangle Ratios 371 4.2.3 Reciprocal Identities 372 4.2.4 Evaluating Trigonometric Functions Exactly for Special Angle Measures 373 4.2.

5 Using Calculators to Evaluate (Approximate) Trigonometric Function Values 377 4.2.6 Solving a Right Triangle Given an Acute Angle Measure and a Side Length 378 4.3 Trigonometric Functions of Angles 387 4.3.1 Trigonometric Functions: The Cartesian Plane 387 4.3.2 Algebraic Signs of the Trigonometric Functions 390 4.

3.3 Ranges of the Trigonometric Functions 393 4.3.4 Reference Angles and Reference Right Triangles 395 4.3.5 Evaluating Trigonometric Functions for Nonacute Angles 398 4.4 The Law of Sines 405 4.4.

1 Solving Oblique Triangles 405 4.5 The Law of Cosines 418 4.5.1 Solving Oblique Triangles Using the Law of Cosines 419 4.5.2 The Area of a Triangle 423 Review 432 Review Exercises 436 Practice Test 438 Cumulative Test 439 5 Trigonometric Functions of Real Numbers 440 5.1 Trigonometric Functions: The Unit Circle Approach 441 5.1.

1 Trigonometric Functions and the Unit Circle (Circular Functions) 441 5.1.2 Properties of Trigonometric (Circular) Functions 444 5.2 Graphs of Sine and Cosine Functions 451 5.2.1 The Graphs of Sinusoidal Functions 451 5.2.2 Graphing a Shifted Sinusoidal Function: y = A sin(Bx + C) + D and y = A cos(Bx + C) + D 464 5.

2.3 Harmonic Motion 467 5.2.4 Graphing Sums of Functions: Addition of Ordinates 471 5.3 Graphs of Other Trigonometric Functions 481 5.3.1 Graphing the Tangent, Cotangent, Secant, and Cosecant Functions 481 5.3.

2 Translations of Trigonometric Functions 492 Review 500 Review Exercises 504 Practice Test 505 Cumulative Test 506 6 Analytic Trigonometry 507 6.1 Trigonometric Identities 508 6.1.1 Fundamental Identities 509 6.1.2 Simplifying Trigonometric Identities 511 6.1.3 Verifying Identities 513 6.

2 Sum and Difference Identities 519 6.2.1 Sum and Difference Identities for the Cosine Function 520 6.2.2 Sum and Difference Identities for the Sine Function 523 6.2.3 Sum and Difference Identities for the Tangent Function 526 6.3 Double-Angle and Half-Angle Identities 531 6.

3.1 Applying Double-Angle Identities 531 6.3.2 Applying Half-Angle Identities 536 6.4 Product-to-Sum and Sum-to-Product Identities 547 6.4.1 Product-to-Sum Identities 547 6.4.

2 Sum-to-Product Identities 549 6.5 Inverse Trigonometric Functions 555 6.5.1 Inverse Sine Function 556 6.5.2 Inverse Cosine Function 560 6.5.3 Inverse Tangent Function 563 6.

5.4 Remaining Inverse Trigonometric Functions 565 6.5.5 Finding Exact Values for Expressions Involving Inverse Trigonometric Functions 568 6.6 Trigonometric Equations 576 6.6.1 Solving Trigonometric Equations by Inspection 577 6.6.

2 Solving Trigonometric Equations Using Algebraic Techniques 580 6.6.3 Solving Trigonometric Equations That Require the Use of Inverse Functions 582 6.6 .4 Using Trigonometric Identities to Solve Trigonometric Equations 584 Review 593 Review Exercises 597 Practice Test 600 Cumulative Test 601 7 Vectors, the Complex Plane, and Polar Coordinates 602<.