Preface |
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xiii | |
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Basic Concepts of Algebra |
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1 | (970) |
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2 | (7) |
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Properties of the Real Numbers |
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Integer Exponents, Scientific Notation, and Order of Operations |
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9 | (9) |
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Addition, Subtraction, and Multiplication of Polynomials |
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18 | (5) |
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23 | (9) |
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Terms with Common Factors |
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Trinomials of the Type x2 + bx + c |
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Trinomials of the Type ax2 + bx + c, a ≠ 1 |
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The Basics of Equation Solving |
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32 | (4) |
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Linear and Quadratic Equations |
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36 | (9) |
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The Domain of a Rational Expression |
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Simplifying, Multiplying, and Dividing Rational Expressions |
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Adding and Subtracting Rational Expressions |
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Complex Rational Expressions |
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Radical Notation and Rational Exponents |
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45 | (16) |
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Simplifying Radical Expressions |
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Rationalizing Denominators or Numerators |
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55 | (4) |
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59 | (2) |
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Graphs, Functions, and Models |
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61 | (104) |
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62 | (18) |
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74 | (6) |
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80 | (17) |
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Finding Domains of Functions |
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Visualizing Domain and Range |
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Applications of Functions |
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Linear Functions, Slope, and Applications |
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97 | (18) |
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The Linear Function f(x) = mx + b and Slope |
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Slope-Intercept Equations of Lines |
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Graphing f(x) = mx + b Using m and b |
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Applications of Linear Functions |
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109 | (6) |
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Equations of Lines and Modeling |
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115 | (14) |
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Slope-Intercept Equations of Lines |
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Point-Slope Equations of Lines |
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Linear Equations, Functions, Zeros, and Applications |
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129 | (21) |
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Applications Using Linear Models |
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Zeros of Linear Functions |
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Solving Linear Inequalities |
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150 | (6) |
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156 | (5) |
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161 | (4) |
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165 | (70) |
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Increasing, Decreasing, and Piecewise Functions; Applications |
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166 | (15) |
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Increasing, Decreasing, and Constant Functions |
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Relative Maximum and Minimum Values |
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Applications of Functions |
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Functions Defined Piecewise |
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181 | (8) |
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The Algebra of Functions: Sums, Differences, Products, and Quotients |
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The Composition of Functions |
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189 | (9) |
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The Composition of Functions |
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Decomposing a Function as a Composition |
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Symmetry and Transformations |
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198 | (21) |
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Transformations of Functions |
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Vertical and Horizontal Translations |
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Vertical and Horizontal Stretchings and Shrinkings |
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213 | (6) |
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Variation and Applications |
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219 | (16) |
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228 | (4) |
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232 | (3) |
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Quadratic Functions and Equations; Inequalities |
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235 | (60) |
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236 | (8) |
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The Complex-Number System |
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Quadratic Equations, Functions, Zeros, and Models |
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244 | (17) |
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Quadratic Equations and Quadratic Functions |
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Using the Quadratic Formula |
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Equations Reducible to Quadratic |
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Analyzing Graphs of Quadratic Functions |
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261 | (15) |
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Graphing Quadratic Functions of the Type f(x) = a(x -- h)2 + k |
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Graphing Quadratic Functions of the Type f(x) = ax2 + bx + c, ≠ 0 |
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271 | (5) |
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Solving Rational Equations and Radical Equations |
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276 | (8) |
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Solving Equations and Inequalities with Absolute Value |
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284 | (11) |
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Equations with Absolute Value |
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Inequalities with Absolute Value |
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289 | (4) |
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293 | (2) |
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Polynomial and Rational Functions |
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295 | (84) |
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Polynomial Functions and Modeling |
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296 | (17) |
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Finding Zeros of Factored Polynomial Functions |
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Finding Real Zeros on a Calculator |
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Graphing Polynomial Functions |
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313 | (10) |
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Graphing Polynomial Functions |
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The Intermediate Value Theorem |
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320 | (3) |
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Polynomial Division; The Remainder and Factor Theorems |
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323 | (9) |
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The Remainder Theorem and Synthetic Division |
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Finding Factors of Polynomials |
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Theorems about Zeros of Polynomial Functions |
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332 | (10) |
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The Fundamental Theorem of Algebra |
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Finding Polynomials with Given Zeros |
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Zeros of Polynomial Functions with Real Coefficients |
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Integer Coefficients and the Rational Zeros Theorem |
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342 | (18) |
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The Domain of a Rational Function |
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356 | (4) |
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Polynomial and Rational Inequalities |
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360 | (19) |
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372 | (5) |
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377 | (2) |
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Exponential and Logarithmic Functions |
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379 | (92) |
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380 | (14) |
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Inverses and One-to-One Functions |
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Finding Formulas for Inverses |
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Inverse Functions and Composition |
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Exponential Functions and Graphs |
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394 | (14) |
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Graphing Exponential Functions |
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Graphs of Exponential Functions, Base e |
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Logarithmic Functions and Graphs |
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408 | (18) |
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Finding Certain Logarithms |
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Converting Between Exponential Equations and Logarithmic Equations |
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Finding Logarithms on a Calculator |
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Changing Logarithmic Bases |
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Graphs of Logarithmic Functions |
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422 | (4) |
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Properties of Logarithmic Functions |
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426 | (9) |
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Simplifying Expressions of the Type loga ax and alogax |
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Solving Exponential and Logarithmic Equations |
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435 | (11) |
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Solving Exponential Equations |
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Solving Logarithmic Equations |
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Applications and Models: Growth and Decay; Compound Interest |
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446 | (25) |
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Interest Compounded Continuously |
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Exponential and Logarithmic Curve Fitting |
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464 | (5) |
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469 | (2) |
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The Trigonometric Functions |
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471 | (102) |
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Trigonometric Functions of Acute Angles |
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472 | (13) |
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The Six Functions Related |
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Function Values of 30°, 45°, and 60° |
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Function Values of Any Acute Angle |
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Cofunctions and Complements |
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Applications of Right Triangles |
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485 | (13) |
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Trigonometric Functions of Any Angle |
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498 | (16) |
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Angles, Rotations, and Degree Measure |
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Trigonometric Functions of Angles or Rotations |
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The Six Functions Related |
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Reference Angles: 30°, 45°, and 60° |
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Function Values for Any Angle |
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Radians, Arc Length, and Angular Speed |
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514 | (16) |
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Distances on the Unit Circle |
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Arc Length and Central Angles |
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Linear Speed and Angular Speed |
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Circular Functions: Graphs and Properties |
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530 | (17) |
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Reflections on the Unit Circle |
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Graphs of the Sine and Cosine Functions |
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Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions |
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Graphs of Transformed Sine and Cosine Functions |
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547 | (26) |
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Variations of Basic Graphs |
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Graphs of Sums: Addition of Ordinates |
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Damped Oscillation: Multiplication of Ordinates |
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561 | (5) |
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566 | (5) |
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571 | (2) |
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Trigonometric Identities, Inverse Functions, and Equations |
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573 | (66) |
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Identities: Pythagorean and Sum and Difference |
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574 | (14) |
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Simplifying Trigonometric Expressions |
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Sum and Difference Identities |
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Identities: Cofunction, Double-Angle, and Half-Angle |
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588 | (10) |
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Proving Trigonometric Identities |
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598 | (8) |
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The Logic of Proving Identities |
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Product-to-Sum and Sum-to-Product Identities |
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Inverses of the Trigonometric Functions |
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606 | (12) |
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Restricting Ranges to Define Inverse Functions |
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Composition of Trigonometric Functions and Their Inverses |
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Solving Trigonometric Equations |
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618 | (21) |
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629 | (4) |
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633 | (5) |
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638 | (1) |
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Applications of Trigonometry |
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639 | (80) |
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640 | (14) |
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Solving Oblique Triangles |
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Solving Triangles (AAS and ASA) |
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654 | (10) |
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Complex Numbers: Trigonometric Form |
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664 | (12) |
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Trigonometric Notation for Complex Numbers |
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Multiplication and Division with Trigonometric Notation |
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Powers of Complex Numbers |
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Polar Coordinates and Graphs |
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676 | (12) |
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Polar and Rectangular Equations |
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685 | (3) |
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688 | (9) |
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697 | (22) |
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712 | (5) |
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717 | (2) |
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Systems of Equations and Matrices |
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719 | (94) |
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Systems of Equations in Two Variables |
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720 | (16) |
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Solving Systems of Equations Graphically |
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730 | (6) |
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Systems of Equations in Three Variables |
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736 | (12) |
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Solving Systems of Equations in Three Variables |
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Mathematical Models and Applications |
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Matrices and Systems of Equations |
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748 | (8) |
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Matrices and Row-Equivalent Operations |
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Gaussian Elimination with Matrices |
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756 | (12) |
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Matrix Addition and Subtraction |
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768 | (8) |
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Solving Systems of Equations |
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Determinants and Cramer's Rule |
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776 | (8) |
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Determinants of Square Matrices |
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Evaluating Determinants Using Cofactors |
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Systems of Inequalities and Linear Programming |
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784 | (14) |
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Graphs of Linear Inequalities |
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Systems of Linear Inequalities |
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Applications: Linear Programming |
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798 | (15) |
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Partial Fraction Decompositions |
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805 | (6) |
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811 | (2) |
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813 | (76) |
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814 | (8) |
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Finding Standard Form by Completing the Square |
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The Circle and the Ellipse |
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822 | (11) |
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833 | (10) |
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Standard Equations of Hyperbolas |
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Nonlinear Systems of Equations and Inequalities |
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843 | (12) |
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Nonlinear Systems of Equations |
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Modeling and Problem Solving |
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Nonlinear Systems of Inequalities |
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850 | (5) |
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855 | (10) |
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Polar Equations of Conics |
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865 | (7) |
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Polar Equations of Conics |
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Converting from Polar Equations to Rectangular Equations |
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Finding Polar Equations of Conics |
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872 | (17) |
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Graphing Parametric Equations |
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Determining a Rectangular Equation for Given Parametric Equations |
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Determining Parametric Equations for a Given Rectangular Equation |
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881 | (5) |
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886 | (3) |
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Sequences, Series, and Combinatorics |
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889 | (82) |
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890 | (10) |
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Arithmetic Sequences and Series |
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900 | (10) |
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Sum of the First n Terms of an Arithmetic Sequence |
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Geometric Sequences and Series |
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910 | (12) |
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Sum of the First n Terms of a Geometric Sequence |
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Infinite Geometric Series |
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918 | (4) |
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922 | (6) |
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Proving Infinite Sequences of Statements |
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Combinatorics: Permutations |
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928 | (10) |
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Permutations of n Objects Taken k at a Time |
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Permutations of Sets with Nondistinguishable Objects |
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Combinatorics: Combinations |
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938 | (8) |
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946 | (8) |
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Binomial Expansions Using Pascal's Triangle |
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Binomial Expansion Using Factorial Notation |
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954 | (17) |
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Experimental and Theoretical Probability |
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Computing Experimental Probabilities |
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965 | (4) |
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969 | (2) |
Appendix: Basic Concepts from Geometry |
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971 | (22) |
Photo Credits |
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993 | |
Answers |
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1 | (1) |
Index |
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1 | (14) |
Index of Applications |
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15 | |
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The TI-83 Plus and TI-84 Plus Graphing Calculators |
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1 | (76) |
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The TI-89 Graphing Calculator |
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77 | |
TI-83 Plus and TI-84 Plus Index |
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1 | (6) |
TI-89 Index |
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7 | |