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2 | (10) |
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Representing Real Numbers |
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Order and Interval Notation |
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Basic Properties of Algebra |
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P.2 Cartesian Coordinate System |
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12 | (9) |
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Absolute Value of a Real Number |
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P.3 Linear Equations and Inequalities |
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21 | (7) |
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Linear Equations in One Variable |
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Linear Inequalities in One Variable |
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28 | (12) |
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Point-Slope Form Equation of a Line |
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Slope-Intercept Form Equation of a Line |
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Graphing Linear Equations in Two Variables |
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Parallel and Perpendicular Lines |
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Applying Linear Equations in Two Variables |
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P.5 Solving Equations Graphically, Numerically, and Algebraically |
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|
40 | (9) |
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Solving Equations Graphically |
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Solving Quadratic Equations |
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Approximating Solutions of Equations Graphically |
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|
Approximating Solutions of Equations Numerically with Tables |
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Solving Equations by Finding Intersections |
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|
49 | (5) |
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Operations with Complex Numbers |
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Complex Conjugates and Division |
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Complex Solutions of Quadratic Equations |
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|
P.7 Solving Inequalities Algebraically and Graphically |
|
|
54 | (10) |
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Solving Absolute Value Inequalities |
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Solving Quadratic Inequalities |
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Approximating Solutions to Inequalities |
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59 | (1) |
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60 | (4) |
|
Chapter 1 Functions and Graphs |
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1.1 Modeling and Equation Solving |
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64 | (16) |
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Grapher Failure and Hidden Behavior |
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1.2 Functions and Their Properties |
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80 | (19) |
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Function Definition and Notation |
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Increasing and Decreasing Functions |
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Local and Absolute Extrema |
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1.3 Twelve Basic Functions |
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99 | (11) |
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Analyzing Functions Graphically |
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1.4 Building Functions from Functions |
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110 | (9) |
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Combining Functions Algebraically |
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Relations and Implicitly Defined Functions |
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1.5 Parametric Relations and Inverses |
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119 | (10) |
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Relations Defined Parametrically |
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Inverse Relations and Inverse Functions |
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1.6 Graphical Transformations |
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129 | (11) |
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Vertical and Horizontal Translations |
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Vertical and Horizontal Stretches and Shrinks |
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Combining Transformations |
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1.7 Modeling with Functions |
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140 | (18) |
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Functions from Verbal Descriptions |
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152 | (1) |
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152 | (4) |
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156 | (2) |
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Chapter 2 Polynomial, Power, and Rational Functions |
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2.1 Linear and Quadratic Functions and Modeling |
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158 | (16) |
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Linear Functions and Their Graphs |
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Linear Correlation and Modeling |
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Quadratic Functions and Their Graphs |
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Applications of Quadratic Functions |
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2.2 Power Functions with Modeling |
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174 | (11) |
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Power Functions and Variation |
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Monomial Functions and Their Graphs |
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Graphs of Power Functions |
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Modeling with Power Functions |
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2.3 Polynomial Functions of Higher Degree with Modeling |
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|
185 | (12) |
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Graphs of Polynomial Functions |
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End Behavior of Polynomial Functions |
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Zeros of Polynomial Functions |
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Intermediate Value Theorem |
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2.4 Real Zeros of Polynomial Functions |
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197 | (13) |
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Long Division and the Division Algorithm |
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Remainder and Factor Theorems |
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2.5 Complex Zeros and the Fundamental Theorem of Algebra |
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210 | (8) |
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Factoring with Real Number Coefficients |
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2.6 Graphs of Rational Functions |
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218 | (10) |
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Transformations of the Reciprocal Function |
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Analyzing Graphs of Rational Functions |
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Exploring Relative Humidity |
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2.7 Solving Equations in One Variable |
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228 | (8) |
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Solving Rational Equations |
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2.8 Solving Inequalities in One Variable |
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236 | (16) |
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245 | (1) |
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246 | (4) |
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250 | (2) |
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Chapter 3 Exponential, Logistic, and Logarithmic Functions |
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3.1 Exponential and Logistic Functions |
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|
252 | (13) |
|
Exponential Functions and Their Graphs |
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Logistic Functions and Their Graphs |
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3.2 Exponential and Logistic Modeling |
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|
265 | (9) |
|
Constant Percentage Rate and Exponential Functions |
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Exponential Growth and Decay Models |
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|
Using Regression to Model Population |
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|
3.3 Logarithmic Functions and Their Graphs |
|
|
274 | (9) |
|
Inverses of Exponential Functions |
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Common Logarithms---Base 10 |
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Natural Logarithms---Base e |
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|
Graphs of Logarithmic Functions |
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|
|
Measuring Sound Using Decibels |
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|
3.4 Properties of Logarithmic Functions |
|
|
283 | (9) |
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Graphs of Logarithmic Functions with Base b |
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3.5 Equation Solving and Modeling |
|
|
292 | (12) |
|
Solving Exponential Equations |
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|
Solving Logarithmic Equations |
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|
|
Orders of Magnitude and Logarithmic Models |
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|
Logarithmic Re-expression |
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|
|
3.6 Mathematics of Finance |
|
|
304 | (16) |
|
Interest Compounded Annually |
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Interest Compounded k Times per Year |
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Interest Compounded Continuously |
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|
Loans and Mortgages---Present Value |
|
|
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|
313 | (1) |
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314 | (4) |
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318 | (2) |
|
Chapter 4 Trigonometric Functions |
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4.1 Angles and Their Measures |
|
|
320 | (9) |
|
The Problem of Angular Measure |
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|
Angular and Linear Motion |
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|
4.2 Trigonometric Functions of Acute Angles |
|
|
329 | (9) |
|
Right Triangle Trigonometry |
|
|
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|
|
|
Evaluating Trigonometric Functions with a Calculator |
|
|
|
Common Calculator Errors When Evaluating Trig Functions |
|
|
|
Applications of Right Triangle Trigonometry |
|
|
|
4.3 Trigonometry Extended: The Circular Functions |
|
|
338 | (12) |
|
Trigonometric Functions of Any Angle |
|
|
|
Trigonometric Functions of Real Numbers |
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|
4.4 Graphs of Sine and Cosine: Sinusoids |
|
|
350 | (11) |
|
The Basic Waves Revisited |
|
|
|
Sinusoids and Transformations |
|
|
|
Modeling Periodic Behavior with Sinusoids |
|
|
|
4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant |
|
|
361 | (8) |
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|
4.6 Graphs of Composite Trigonometric Functions |
|
|
369 | (9) |
|
Combining Trigonometric and Algebraic Functions |
|
|
|
Sums and Differences of Sinusoids |
|
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|
|
|
4.7 Inverse Trigonometric Functions |
|
|
378 | (10) |
|
|
|
|
Inverse Cosine and Tangent Functions |
|
|
|
Composing Trigonometric and Inverse Trigonometric Functions |
|
|
|
Applications of Inverse Trigonometric Functions |
|
|
|
4.8 Solving Problems with Trigonometry |
|
|
388 | (16) |
|
More Right Triangle Problems |
|
|
|
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|
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|
|
399 | (1) |
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|
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399 | (3) |
|
|
|
402 | (2) |
|
Chapter 5 Analytic Trigonometry |
|
|
|
5.1 Fundamental Identities |
|
|
404 | (9) |
|
|
|
|
Basic Trigonometric Identities |
|
|
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|
Simplifying Trigonometric Expressions |
|
|
|
Solving Trigonometric Equations |
|
|
|
5.2 Proving Trigonometric Identities |
|
|
413 | (8) |
|
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|
|
Disproving Non-Identities |
|
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|
|
|
5.3 Sum and Difference Identities |
|
|
421 | (7) |
|
|
|
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|
|
|
Sine of a Difference or Sum |
|
|
|
Tangent of a Difference or Sum |
|
|
|
Verifying a Sinusoid Algebraically |
|
|
|
5.4 Multiple-Angle Identities |
|
|
428 | (6) |
|
|
|
|
Power-Reducing Identities |
|
|
|
|
|
|
Solving Trigonometric Equations |
|
|
|
|
|
434 | (8) |
|
Deriving the Law of Sines |
|
|
|
Solving Triangles (AAS, ASA) |
|
|
|
|
|
|
|
|
|
|
|
442 | (14) |
|
Deriving the Law of Cosines |
|
|
|
Solving Triangles (SAS, SSS) |
|
|
|
Triangle Area and Heron's Formula |
|
|
|
|
|
|
|
|
450 | (1) |
|
|
|
450 | (4) |
|
|
|
454 | (2) |
|
Chapter 6 Applications of Trigonometry |
|
|
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|
456 | (11) |
|
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|
6.2 Dot Product of Vectors |
|
|
467 | (8) |
|
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|
|
Projecting One Vector onto Another |
|
|
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|
|
|
6.3 Parametric Equations and Motion |
|
|
475 | (12) |
|
|
|
|
|
|
|
Eliminating the Parameter |
|
|
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|
|
Simulating Motion with a Grapher |
|
|
|
|
|
487 | (7) |
|
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|
|
Finding Distance Using Polar Coordinates |
|
|
|
6.5 Graphs of Polar Equations |
|
|
494 | (9) |
|
Polar Curves and Parametric Curves |
|
|
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|
|
6.6 De Moivre's Theorem and nth Roots |
|
|
503 | (17) |
|
|
|
|
Trigonometric Form of Complex Numbers |
|
|
|
Multiplication and Division of Complex Numbers |
|
|
|
Powers of Complex Numbers |
|
|
|
|
|
|
|
|
513 | (1) |
|
|
|
514 | (3) |
|
|
|
517 | (3) |
|
Chapter 7 Systems and Matrices |
|
|
|
7.1 Solving Systems of Two Equations |
|
|
520 | (10) |
|
The Method of Substitution |
|
|
|
Solving Systems Graphically |
|
|
|
The Method of Elimination |
|
|
|
|
|
|
|
|
530 | (14) |
|
|
|
|
Matrix Addition and Subtraction |
|
|
|
|
|
|
Identity and Inverse Matrices |
|
|
|
Determinant of a Square Matrix |
|
|
|
|
|
|
7.3 Multivariate Linear Systems and Row Operations |
|
|
544 | (13) |
|
Triangular Form for Linear Systems |
|
|
|
|
|
|
Elementary Row Operations and Row Echelon Form |
|
|
|
|
|
|
Solving Systems with Inverse Matrices |
|
|
|
|
|
|
|
|
557 | (8) |
|
Partial Fraction Decomposition |
|
|
|
Denominators with Linear Factors |
|
|
|
Denominators with Irreducible Quadratic Factors |
|
|
|
|
|
|
7.5 Systems of Inequalities in Two Variables |
|
|
565 | (15) |
|
|
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|
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|
|
573 | (1) |
|
|
|
573 | (4) |
|
|
|
577 | (3) |
|
Chapter 8 Analytic Geometry in Two and Three Dimensions |
|
|
|
8.1 Conic Sections and Parabolas |
|
|
580 | (11) |
|
|
|
|
|
|
|
Translations of Parabolas |
|
|
|
Reflective Property of a Parabola |
|
|
|
|
|
591 | (11) |
|
|
|
|
|
|
|
|
|
|
Reflective Property of an Ellipse |
|
|
|
|
|
602 | (10) |
|
|
|
|
Translations of Hyperbolas |
|
|
|
|
|
|
Reflective Property of a Hyperbola |
|
|
|
|
|
|
8.4 Translation and Rotation of Axes |
|
|
612 | (8) |
|
Second-Degree Equations in Two Variables |
|
|
|
Translating Axes Versus Translating Graphs |
|
|
|
|
|
|
|
|
|
8.5 Polar Equations of Conics |
|
|
620 | (9) |
|
|
|
|
Writing Polar Equations for Conics |
|
|
|
Analyzing Polar Equations of Conics |
|
|
|
|
|
|
8.6 Three-Dimensional Cartesian Coordinate System |
|
|
629 | (13) |
|
Three-Dimensional Cartesian Coordinates |
|
|
|
Distance and Midpoint Formulas |
|
|
|
|
|
|
Planes and Other Surfaces |
|
|
|
|
|
|
|
|
|
|
|
637 | (1) |
|
|
|
638 | (2) |
|
|
|
640 | (2) |
|
Chapter 9 Discrete Mathematics |
|
|
|
|
|
642 | (10) |
|
Discrete Versus Continuous |
|
|
|
The Importance of Counting |
|
|
|
The Multiplication Principle of Counting |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
652 | (6) |
|
|
|
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|
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|
|
|
|
|
|
|
|
658 | (12) |
|
Sample Spaces and Probability Functions |
|
|
|
Determining Probabilities |
|
|
|
Venn Diagrams and Tree Diagrams |
|
|
|
|
|
|
|
|
|
|
|
670 | (8) |
|
|
|
|
Limits of Infinite Sequences |
|
|
|
Arithmetic and Geometric Sequences |
|
|
|
Sequences and Graphing Calculators |
|
|
|
|
|
678 | (9) |
|
|
|
|
Sums of Arithmetic and Geometric Sequences |
|
|
|
|
|
|
Convergence of Geometric Series |
|
|
|
9.6 Mathematical Induction |
|
|
687 | (6) |
|
The Tower of Hanoi Problem |
|
|
|
Principle of Mathematical Induction |
|
|
|
|
|
|
9.7 Statistics and Data (Graphical) |
|
|
693 | (11) |
|
|
|
|
Displaying Categorical Data |
|
|
|
|
|
|
|
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|
|
|
9.8 Statistics and Data (Algebraic) |
|
|
704 | (13) |
|
Parameters and Statistics |
|
|
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|
|
|
|
|
|
|
|
|
Variance and Standard Deviation |
|
|
|
|
|
|
|
|
717 | (19) |
|
The Many Misuses of Statistics |
|
|
|
|
|
|
The Importance of Randomness |
|
|
|
Surveys and Observational Studies |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
729 | (1) |
|
|
|
729 | (4) |
|
|
|
733 | (3) |
|
Chapter 10 An Introduction to Calculus: Limits, Derivatives, and Integrals |
|
|
|
10.1 Limits and Motion: The Tangent Problem |
|
|
736 | (11) |
|
|
|
|
|
|
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|
|
|
The Connection to Tangent Lines |
|
|
|
|
|
|
10.2 Limits and Motion: The Area Problem |
|
|
747 | (8) |
|
Distance from a Constant Velocity |
|
|
|
Distance from a Changing Velocity |
|
|
|
|
|
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|
|
|
|
|
755 | (11) |
|
|
|
|
Defining a Limit Informally |
|
|
|
|
|
|
Limits of Continuous Functions |
|
|
|
One-Sided and Two-Sided Limits |
|
|
|
Limits Involving Infinity |
|
|
|
10.4 Numerical Derivatives and Integrals |
|
|
766 | (13) |
|
Derivatives on a Calculator |
|
|
|
Definite Integrals on a Calculator |
|
|
|
Computing a Derivative from Data |
|
|
|
Computing a Definite Integral from Data |
|
|
|
|
|
775 | (1) |
|
|
|
775 | (2) |
|
|
|
777 | (2) |
|
APPENDIX A Algebra Review |
|
|
|
A.1 Radicals and Rational Exponents |
|
|
779 | (5) |
|
|
|
|
Simplifying Radical Expressions |
|
|
|
Rationalizing the Denominator |
|
|
|
|
|
|
A.2 Polynomials and Factoring |
|
|
784 | (7) |
|
Adding, Subtracting, and Multiplying Polynomials |
|
|
|
|
|
|
Factoring Polynomials Using Special Products |
|
|
|
|
|
|
|
|
|
A.3 Fractional Expressions |
|
|
791 | (5) |
|
Domain of an Algebraic Expression |
|
|
|
Reducing Rational Expressions |
|
|
|
Operations with Rational Expressions |
|
|
|
Compound Rational Expressions |
|
|
|
|
|
|
B.1 Formulas from Algebra |
|
|
796 | (1) |
|
|
|
|
Radicals and Rational Exponents |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Arithmetic Sequences and Series |
|
|
|
Geometric Sequences and Series |
|
|
|
|
|
|
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|
|
|
|
B.2 Formulas from Geometry |
|
|
797 | (1) |
|
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|
|
B.3 Formulas from Trigonometry |
|
|
797 | (2) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Sum and Difference Identities |
|
|
|
|
|
|
|
|
|
Power-Reducing Identities |
|
|
|
|
|
|
|
|
|
Trigonometric Form of a Complex Number |
|
|
|
|
|
|
B.4 Formulas from Analytic Geometry |
|
|
799 | (1) |
|
|
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|
|
|
Parabolas with Vertex (h, k) |
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Ellipses with Center (h, k) and a > b > 0 |
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Hyperbolas with Center (h, k) |
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|
|
B.5 Gallery of Basic Functions |
|
|
800 | (1) |
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|
|
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C.1 Logic: An Introduction |
|
|
801 | (6) |
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|
|
|
|
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C.2 Conditionals and Biconditionals |
|
|
807 | (7) |
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|
| Bibliography |
|
814 | (2) |
| Glossary |
|
816 | (17) |
| Selected Answers |
|
833 | (102) |
| Applications Index |
|
935 | (4) |
| Index |
|
939 | |
