Preface |
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xi | |
To the Student |
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xix | |
Interactive Figures Index |
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xx | |
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R Basic Concepts of Algebra |
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1 | (990) |
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R.1 The Real-Number System |
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2 | (6) |
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Real Numbers / Interval Notation / Properties of the Real Numbers / Absolute Value |
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R.2 Integer Exponents, Scientific Notation, and Order of Operations |
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8 | (9) |
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Integers as Exponents / Scientific Notation / Order of Operations |
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R.3 Addition, Subtraction, and Multiplication of Polynomials |
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17 | (5) |
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Polynomials / Addition and Subtraction / Multiplication |
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22 | (8) |
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Terms with Common Factors / Factoring by Grouping / Trinomials of the Type x2 + bx + c / Trinomials of the Type ax2 + bx + c, a ≠ 1 / Special Factorizations |
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R.5 The Basics of Equation Solving |
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30 | (5) |
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Linear Equations and Quadratic Equations / Formulas |
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35 | (9) |
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The Domain of a Rational Expression / Simplifying, Multiplying, and Dividing Rational Expressions / Adding and Subtracting Rational Expressions / Complex Rational Expressions |
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R.7 Radical Notation and Rational Exponents |
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44 | (13) |
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Simplifying Radical Expressions / An Application / Rationalizing Denominators or Numerators / Rational Exponents |
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53 | (1) |
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54 | (2) |
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56 | (1) |
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1 Graphs, Functions, and Models |
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57 | (102) |
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1.1 Introduction to Graphing |
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58 | (16) |
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Graphs / Solutions of Equations / Graphs of Equations / The Distance Formula / Midpoints of Segments / Circles |
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69 | (5) |
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74 | (16) |
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Functions / Notation for Functions / Graphs of Functions / Finding Domains of Functions / Visualizing Domain and Range / Applications of Functions |
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1.3 Linear Functions, Slope, and Applications |
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90 | (17) |
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Linear Functions / The Linear Function f(x) = mx + b and Slope / Applications of Slope / Slope-Intercept Equations of Lines / Graphing f(x) = mx + b Using m and b / Applications of Linear Functions |
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101 | (5) |
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106 | (1) |
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1.4 Equations of Lines and Modeling |
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107 | (14) |
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Slope-Intercept Equations of Lines / Point-Slope Equations of Lines / Parallel Lines / Perpendicular Lines / Mathematical Models / Curve Fitting / Linear Regression |
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1.5 Linear Equations, Functions, Zeros, and Applications |
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121 | (18) |
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Linear Equations / Applications Using Linear Models / Zeros of Linear Functions |
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1.6 Solving Linear Inequalities |
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139 | (20) |
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Linear Inequalities / Compound Inequalities / An Application |
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144 | (7) |
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151 | (4) |
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155 | (4) |
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159 | (76) |
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2.1 Increasing, Decreasing, and Piecewise Functions; Applications |
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160 | (15) |
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Increasing, Decreasing, and Constant Functions / Relative Maximum and Minimum Values / Applications of Functions / Functions Defined Piecewise |
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2.2 The Algebra of Functions |
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175 | (7) |
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The Algebra of Functions: Sums, Differences, Products, and Quotients / Difference Quotients |
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2.3 The Composition of Functions |
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182 | (10) |
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The Composition of Functions / Decomposing a Function as a Composition |
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190 | (2) |
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192 | (7) |
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Symmetry / Even Functions and Odd Functions |
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199 | (14) |
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Transformations of Functions / Vertical Translations and Horizontal Translations / Reflections / Vertical and Horizontal Stretchings and Shrinkings |
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209 | (4) |
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2.6 Variation and Applications |
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213 | (22) |
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Direct Variation / Inverse Variation / Combined Variation |
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222 | (7) |
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229 | (4) |
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233 | (2) |
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3 Quadratic Functions and Equations; Inequalities |
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235 | (62) |
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236 | (7) |
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The Complex-Number System / Addition and Subtraction / Multiplication / Conjugates and Division |
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3.2 Quadratic Equations, Functions, Zeros, and Models |
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243 | (16) |
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Quadratic Equations and Quadratic Functions / Completing the Square / Using the Quadratic Formula / The Discriminant / Equations Reducible to Quadratic / Applications |
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3.3 Analyzing Graphs of Quadratic Functions |
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259 | (16) |
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Graphing Quadratic Functions of the Type f(x) = a(x - h)2 + k / Graphing Quadratic Functions of the Type f{x) = ax2 + bx + c, a ≠ 0 / Applications |
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269 | (4) |
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273 | (2) |
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3.4 Solving Rational Equations and Radical Equations |
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275 | (8) |
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Rational Equations / Radical Equations |
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3.5 Solving Equations and Inequalities with Absolute Value |
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283 | (14) |
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Equations with Absolute Value / Inequalities with Absolute Value |
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287 | (6) |
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293 | (2) |
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295 | (2) |
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4 Polynomial Functions and Rational Functions |
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297 | (94) |
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4.1 Polynomial Functions and Modeling |
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298 | (17) |
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The Leading-Term Test / Finding Zeros of Factored Polynomial Functions / Finding Real Zeros on a Calculator / Polynomial Models |
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4.2 Graphing Polynomial Functions |
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315 | (10) |
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Graphing Polynomial Functions / The Intermediate Value Theorem |
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322 | (3) |
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4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem |
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325 | (10) |
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Division and Factors / The Remainder Theorem and Synthetic Division / Finding Factors of Polynomials |
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333 | (2) |
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4.4 Theorems about Zeros of Polynomial Functions |
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335 | (10) |
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The Fundamental Theorem of Algebra / Finding Polynomials with Given Zeros / Zeros of Polynomial Functions with Real Coefficients / Rational Coefficients / Integer Coefficients and the Rational Zeros Theorem / Descartes' Rule of Signs |
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345 | (20) |
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The Domain of a Rational Function / Asymptotes / Applications |
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361 | (4) |
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4.6 Polynomial Inequalities and Rational Inequalities |
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365 | (26) |
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Polynomial Inequalities / Rational Inequalities |
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375 | (10) |
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385 | (4) |
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389 | (2) |
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5 Exponential Functions and Logarithmic Functions |
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391 | (92) |
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392 | (12) |
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Inverses / Inverses and One-to-One Functions / Finding Formulas for Inverses / Inverse Functions and Composition / Restricting a Domain |
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5.2 Exponential Functions and Graphs |
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404 | (13) |
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Graphing Exponential Functions / Applications / The Number e / Graphs of Exponential Functions, Base e |
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5.3 Logarithmic Functions and Graphs |
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417 | (18) |
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Logarithmic Functions / Finding Certain Logarithms / Converting Between Exponential Equations and Logarithmic Equations / Finding Logarithms on a Calculator / Natural Logarithms / Changing Logarithmic Bases / Graphs of Logarithmic Functions / Applications |
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429 | (4) |
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433 | (2) |
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5.4 Properties of Logarithmic Functions |
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435 | (8) |
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Logarithms of Products / Logarithms of Powers / Logarithms of Quotients / Applying the Properties / Simplifying Expressions of the Type loga ax and alogax |
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5.5 Solving Exponential Equations and Logarithmic Equations |
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443 | (10) |
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Solving Exponential Equations / Solving Logarithmic Equations |
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5.6 Applications and Models: Growth and Decay; Compound Interest |
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453 | (30) |
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Population Growth / Interest Compounded Continuously / Models of Limited Growth / Exponential Decay / Exponential and Logarithmic Curve Fitting |
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470 | (7) |
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477 | (4) |
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481 | (2) |
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6 The Trigonometric Functions |
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483 | (106) |
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6.1 Trigonometric Functions of Acute Angles |
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484 | (12) |
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The Trigonometric Ratios / The Six Functions Related / Function Values of 30°, 45°, and 60° / Function Values of Any Acute Angle / Cofunctions and Complements |
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6.2 Applications of Right Triangles |
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496 | (13) |
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Solving Right Triangles / Applications |
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6.3 Trigonometric Functions of Any Angle |
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509 | (18) |
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Angles, Rotations, and Degree Measure / Trigonometric Functions of Angles or Rotations / The Six Functions Related / Terminal Side on an Axis / Reference Angles: 30°, 45°, and 60° / Function Values for Any Angle |
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525 | (2) |
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6.4 Radians, Arc Length, and Angular Speed |
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527 | (15) |
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Distances on the Unit Circle / Radian Measure / Arc Length and Central Angles / Linear Speed and Angular Speed |
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6.5 Circular Functions: Graphs and Properties |
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542 | (15) |
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Reflections on the Unit Circle / Finding Function Values / Graphs of the Sine and Cosine Functions / Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions |
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6.6 Graphs of Transformed Sine Functions and Cosine Functions |
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557 | (32) |
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Variations of Basic Graphs / Graphs of Sums: Addition of Ordinates / Damped Oscillation: Multiplication of Ordinates |
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570 | (4) |
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574 | (10) |
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584 | (3) |
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587 | (2) |
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7 Trigonometric Identities, Inverse Functions, and Equations |
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589 | (66) |
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7.1 Identities: Pythagorean and Sum and Difference |
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590 | (13) |
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Pythagorean Identities / Simplifying Trigonometric Expressions / Sum and Difference Identities |
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7.2 Identities: Cofunction, Double-Angle, and Half-Angle |
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603 | (9) |
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Cofunction Identities / Double-Angle Identities / Half-Angle Identities |
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7.3 Proving Trigonometric Identities |
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612 | (9) |
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The Logic of Proving Identities / Proving Identities / Product-to-Sum and Sum-to-Product Identities |
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619 | (2) |
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7.4 Inverses of the Trigonometric Functions |
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621 | (11) |
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Restricting Ranges to Define Inverse Functions / Composition of Trigonometric Functions and Their Inverses |
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7.5 Solving Trigonometric Equations |
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632 | (23) |
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640 | (4) |
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644 | (7) |
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651 | (3) |
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654 | (1) |
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8 Applications of Trigonometry |
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655 | (86) |
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656 | (13) |
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Solving Oblique Triangles / The Law of Sines / Solving Triangles (AAS and ASA) / Solving Triangles (SSA) / The Area of a Triangle |
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669 | (10) |
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The Law of Cosines / Solving Triangles (SAS) / Solving Triangles (SSS) |
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8.3 Complex Numbers: Trigonometric Notation |
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679 | (12) |
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Graphical Representation / Trigonometric Notation for Complex Numbers / Multiplication and Division with Trigonometric Notation / Powers of Complex Numbers / Roots of Complex Numbers |
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689 | (2) |
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8.4 Polar Coordinates and Graphs |
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691 | (11) |
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Polar Coordinates / Polar Equations and Rectangular Equations / Graphing Polar Equations |
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699 | (3) |
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8.5 Vectors and Applications |
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702 | (8) |
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Vectors / Vector Addition / Applications / Components |
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710 | (31) |
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Position Vectors / Operations on Vectors / Unit Vectors / Direction Angles / Angle Between Vectors / Forces in Equilibrium |
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725 | (11) |
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736 | (4) |
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740 | (1) |
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9 Systems of Equations and Matrices |
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741 | (94) |
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9.1 Systems of Equations in Two Variables |
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742 | (16) |
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Solving Systems of Equations Graphically / The Substitution Method / The Elimination Method / Applications |
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752 | (6) |
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9.2 Systems of Equations in Three Variables |
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758 | (10) |
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Solving Systems of Equations in Three Variables / Applications / Mathematical Models and Applications |
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9.3 Matrices and Systems of Equations |
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768 | (8) |
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Matrices and Row-Equivalent Operations / Gaussian Elimination with Matrices / Gauss-Jordan Elimination |
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776 | (13) |
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Matrix Addition and Subtraction / Scalar Multiplication / Products of Matrices / Matrix Equations |
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787 | (2) |
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789 | (7) |
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The Identity Matrix / The Inverse of a Matrix / Solving Systems of Equations |
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9.6 Determinants and Cramer's Rule |
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796 | (8) |
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Determinants of Square Matrices / Evaluating Determinants Using Cofactors / Cramer's Rule |
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9.7 Systems of Inequalities and Linear Programming |
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804 | (12) |
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Graphs of Linear Inequalities / Systems of Linear Inequalities / Applications: Linear Programming |
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816 | (19) |
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Partial Fraction Decompositions |
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822 | (6) |
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828 | (4) |
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832 | (3) |
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10 Analytic Geometry Topics |
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835 | (76) |
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836 | (8) |
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Parabolas / Finding Standard Form by Completing the Square / Applications |
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10.2 The Circle and the Ellipse |
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844 | (9) |
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Circles / Ellipses / Applications |
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853 | (10) |
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Standard Equations of Hyperbolas / Applications |
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10.4 Nonlinear Systems of Equations and Inequalities |
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863 | (13) |
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Nonlinear Systems of Equations / Modeling and Problem Solving / Nonlinear Systems of Inequalities |
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870 | (5) |
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875 | (1) |
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876 | (8) |
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Rotation of Axes / The Discriminant |
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10.6 Polar Equations of Conics |
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884 | (6) |
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Polar Equations of Conics / Converting from Polar Equations to Rectangular Equations / Finding Polar Equations of Conics |
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10.7 Parametric Equations |
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890 | (21) |
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Graphing Parametric Equations / Determining a Rectangular Equation for Given Parametric Equations / Determining Parametric Equations for a Given Rectangular Equation / Applications |
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898 | (6) |
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904 | (4) |
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908 | (3) |
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11 Sequences, Series, and Combinatorics |
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911 | (80) |
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11.1 Sequences and Series |
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912 | (8) |
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Sequences / Finding the General Term / Sums and Series / Sigma Notation / Recursive Definitions |
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11.2 Arithmetic Sequences and Series |
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920 | (9) |
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Arithmetic Sequences / Sum of the First n Terms of an Arithmetic Sequence / Applications |
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11.3 Geometric Sequences and Series |
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929 | (12) |
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Geometric Sequences / Sum of the First n Terms of a Geometric Sequence / Infinite Geometric Series / Applications |
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937 | (4) |
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11.4 Mathematical Induction |
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941 | (6) |
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Proving Infinite Sequences of Statements |
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946 | (1) |
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11.5 Combinatorics: Permutations |
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947 | (10) |
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Permutations / Factorial Notation / Permutations of n Objects Taken k at a Time / Permutations of Sets with Nondistinguishable Objects |
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11.6 Combinatorics: Combinations |
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957 | (6) |
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11.7 The Binomial Theorem |
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963 | (8) |
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Binomial Expansions Using Pascal's Triangle / Binomial Expansion Using Combination Notation / Finding a Specific Term / Total Number of Subsets |
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971 | (20) |
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Experimental Probability and Theoretical Probability / Computing Experimental Probabilities / Theoretical Probability |
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981 | (4) |
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985 | (3) |
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988 | (3) |
Photo Credits |
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991 | |
Answers |
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1 | (1) |
Index |
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1 | (12) |
Index of Applications |
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13 | |