1 Functions and Mathematical Models 1 1-1 Functions: Graphically, Algebraically, Numerically, and Verbally 3
1-2 Types of Functions 7
1-3 Dilation and Translation of Function Graphs 15
1-4 Composition of Functions 22
1-5 Inverse of a Function 33
1-6 Reflections, Absolute Values, and Other Transformations 43
1-7 Precalculus Journal 50
1-8 Chapter Review and Test 51
2 Periodic Functions and Right Triangle Problems 59 2-1 Introduction to Periodic Functions 61
2-2 Measurement of Rotation 62
2-3 Sine and Cosine Functions 66
2-4 Values of the Six Trigonometric Functions 73
2-5 Inverse Trigonometric Functions and Triangle Problems 80
2-6 Chapter Review and Test 88
3 Applications of Trigonometric and Circular Functions 93 3-1 Sinusoids: Amplitude, Period, and Cycles 95
3-2 General Sinusoidal Graphs 96
3-3 Graphs of Tangent, Cotangent, Secant, and Cosecant Functions 105
3-4 Radian Measure of Angles 110
3-5 Circular Functions 117
3-6 Inverse Circular Relations: Given y, Find x 124
3-7 Sinusoidal Functions as Mathematical Models 130
3-8 Rotary Motion 138
3-9 Chapter Review and Test 148
4 Trigonometric Function Properties, Identities, and Parametric Functions155
4-1 Introduction to the Pythagorean Property 157
4-2 Pythagorean, Reciprocal, and Quotient Properties 158
4-3 Identities and Algebraic Transformation of Expressions 162
4-4 Arcsine, Arctangent, Arccosine, and Trigonometric Equations 168
4-5 Parametric Function 176
4-6 Inverse Trigonometric Relation Graphs 184
4-7 Chapter Review and Test 191
5 Properties of Combined Sinusoids 195 5-1 Introduction to Combinations of Sinusoids 197
5-2 Composite Argument and Linear Combination Properties 198
5-3 Other Composite Argument Properties 205
5-4 Composition of Ordinates and Harmonic Analysis 213
5-5 The Sum and Product Properties 223
5-6 Double and Half Argument Properties 231
5-7 Chapter Review and Test 239
6 Triangle Trigonometry 247 6-1 Introduction to Oblique Triangles 249
6-2 Oblique Triangles: Law of Cosines 250
6-3 Area of a Triangle 255
6-4 Oblique Triangles: Law of Sines 259
6-5 The Ambiguous Case 263
6-6 Vector Addition 266
6-7 Real-World Triangle Problems 274
6-8 Chapter Review and Test 280
6-9 Cumulative Review, Chapters 1–6 286
15 Polynomial and Rational Functions, Limits, and Derivatives 667
15-1 Review of Polynomial Functions 66915-2 Graphs and Zeros of Polynomial Functions 670
15-3 Fitting Polynomial Functions to Data 680
15-4 Rational Functions: Discontinuities, Limits, and Partial Fractions 687
15-5 Instantaneous Rate of Change of a Function: The Derivative 694
15-6 Chapter Review and Test 702
15-7 Cumulative Review, Chapters 10–15 707
7 Properties of Elementary Functions 291 7-1 Shapes of Function Graphs 293
7-2 Identifying Functions from Graphical Patterns 294
7-3 Identifying Functions from Numerical Patterns 304
7-4 Properties of Logarithms 314
7-5 Logarithms: Equations and Other Bases 321
7-6 Logarithmic Functions 328
7-7 Logistic Functions for Restrained Growth 336
7-8 Chapter Review and Test 343
14 Sequences and Series 637
14-1 Introduction to Sequences and Series 639
14-2 Arithmetic, Geometric, and Other Sequences 640
14-3 Series and Partial Sums 648
14-4 Chapter Review and Test 662
13 Polar Coordinates, Complex Numbers, and Moving Objects 597
13-1 Introduction to Polar Coordinates 599
13-2 Polar Equations of Conics and Other Curves 600
13-3 Intersections of Polar Curves 610
13-4 Complex Numbers in Polar Form 614
13-5 Parametric Equations of Moving Objects 621
13-6 Chapter Review and Test 631
8 Fitting Functions to Data 351
8-1 Introduction to Regression for Linear Data 353
8-2 Deviations, Residuals, and the Correlation Coefficient 354
8-3 Regression for Nonlinear Data 360
8-4 Linearizing Data and Logarithmic Graph Paper 367
8-5 Residual Plots and Mathematical Models 381
8-6 Chapter Review and Test 389
9 Probability, and Functions of a Random Variable 397 9-1 Introduction to Probability 399
9-2 Words Associated with Probability 400
9-3 Two Counting Principles 402
9-4 Probabilities of Various Permutations 407
9-5 Probabilities of Various Combinations 412
9-6 Properties of Probability 420
9-7 Functions of a Random Variable 428
9-8 Mathematical Expectation 434
9-9 Chapter Review and Test 440
9-10 Cumulative Review, Chapters 7–9 445
1-1 Functions: Graphically, Algebraically, Numerically, and Verbally 3
1-2 Types of Functions 7
1-3 Dilation and Translation of Function Graphs 15
1-4 Composition of Functions 22
1-5 Inverse of a Function 33
1-6 Reflections, Absolute Values, and Other Transformations 43
1-7 Precalculus Journal 50
1-8 Chapter Review and Test 51
2 Periodic Functions and Right Triangle Problems 59
2-1 Introduction to Periodic Functions 61
2-2 Measurement of Rotation 62
2-3 Sine and Cosine Functions 66
2-4 Values of the Six Trigonometric Functions 73
2-5 Inverse Trigonometric Functions and Triangle Problems 80
2-6 Chapter Review and Test 88
3 Applications of Trigonometric and Circular Functions 93
3-1 Sinusoids: Amplitude, Period, and Cycles 95
3-2 General Sinusoidal Graphs 96
3-3 Graphs of Tangent, Cotangent, Secant, and Cosecant Functions 105
3-4 Radian Measure of Angles 110
3-5 Circular Functions 117
3-6 Inverse Circular Relations: Given y, Find x 124
3-7 Sinusoidal Functions as Mathematical Models 130
3-8 Rotary Motion 138
3-9 Chapter Review and Test 148
4 Trigonometric Function Properties, Identities, and Parametric Functions 155
4-1 Introduction to the Pythagorean Property 157
4-2 Pythagorean, Reciprocal, and Quotient Properties 158
4-3 Identities and Algebraic Transformation of Expressions 162
4-4 Arcsine, Arctangent, Arccosine, and Trigonometric Equations 168
4-5 Parametric Function 176
4-6 Inverse Trigonometric Relation Graphs 184
4-7 Chapter Review and Test 191
5 Properties of Combined Sinusoids 195
5-1 Introduction to Combinations of Sinusoids 197
5-2 Composite Argument and Linear Combination Properties 198
5-3 Other Composite Argument Properties 205
5-4 Composition of Ordinates and Harmonic Analysis 213
5-5 The Sum and Product Properties 223
5-6 Double and Half Argument Properties 231
5-7 Chapter Review and Test 239
6 Triangle Trigonometry 247
6-1 Introduction to Oblique Triangles 249
6-2 Oblique Triangles: Law of Cosines 250
6-3 Area of a Triangle 255
6-4 Oblique Triangles: Law of Sines 259
6-5 The Ambiguous Case 263
6-6 Vector Addition 266
6-7 Real-World Triangle Problems 274
6-8 Chapter Review and Test 280
6-9 Cumulative Review, Chapters 1–6 286
15 Polynomial and Rational Functions, Limits, and Derivatives 667
15-1 Review of Polynomial Functions 66915-2 Graphs and Zeros of Polynomial Functions 670
15-3 Fitting Polynomial Functions to Data 680
15-4 Rational Functions: Discontinuities, Limits, and Partial Fractions 687
15-5 Instantaneous Rate of Change of a Function: The Derivative 694
15-6 Chapter Review and Test 702
15-7 Cumulative Review, Chapters 10–15 707
7 Properties of Elementary Functions 291
7-1 Shapes of Function Graphs 293
7-2 Identifying Functions from Graphical Patterns 294
7-3 Identifying Functions from Numerical Patterns 304
7-4 Properties of Logarithms 314
7-5 Logarithms: Equations and Other Bases 321
7-6 Logarithmic Functions 328
7-7 Logistic Functions for Restrained Growth 336
7-8 Chapter Review and Test 343
14 Sequences and Series 637
14-1 Introduction to Sequences and Series 639
14-2 Arithmetic, Geometric, and Other Sequences 640
14-3 Series and Partial Sums 648
14-4 Chapter Review and Test 662
13 Polar Coordinates, Complex Numbers, and Moving Objects 597
13-1 Introduction to Polar Coordinates 599
13-2 Polar Equations of Conics and Other Curves 600
13-3 Intersections of Polar Curves 610
13-4 Complex Numbers in Polar Form 614
13-5 Parametric Equations of Moving Objects 621
13-6 Chapter Review and Test 631
8 Fitting Functions to Data 351
8-1 Introduction to Regression for Linear Data 353
8-2 Deviations, Residuals, and the Correlation Coefficient 354
8-3 Regression for Nonlinear Data 360
8-4 Linearizing Data and Logarithmic Graph Paper 367
8-5 Residual Plots and Mathematical Models 381
8-6 Chapter Review and Test 389
9 Probability, and Functions of a Random Variable 397
9-1 Introduction to Probability 399
9-2 Words Associated with Probability 400
9-3 Two Counting Principles 402
9-4 Probabilities of Various Permutations 407
9-5 Probabilities of Various Combinations 412
9-6 Properties of Probability 420
9-7 Functions of a Random Variable 428
9-8 Mathematical Expectation 434
9-9 Chapter Review and Test 440
9-10 Cumulative Review, Chapters 7–9 445