Contents xi 5 Exponential and Logarithmic Functions 272 5.1 Composite Functions 273 Form a Composite Function • Find the Domain of a Composite Function 5.2 One-to-One Functions; Inverse Functions 281 Determine Whether a Function Is One-to-One • Determine the Inverse of a Function Defined by a Mapping or a Set of Ordered Pairs • Obtain the Graph of the Inverse Function from the Graph of a One-to-One Function • Verify that a Function Defined by an Equation Is an Inverse Function • Find the Inverse of a Function Defined by an Equation 5.3 Exponential Functions 294 Evaluate Exponential Functions • Graph Exponential Functions • Define the Number e • Solve Exponential Equations 5.4 Logarithmic Functions 313 Change Exponential Statements to Logarithmic Statements and Logarithmic Statements to Exponential Statements • Evaluate Logarithmic Expressions • Determine the Domain of a Logarithmic Function • Graph Logarithmic Functions • Solve Logarithmic Equations 5.5 Properties of Logarithms 327 Work with the Properties of Logarithms • Write a Logarithmic Expression as a Sum or Difference of Logarithms • Write a Logarithmic Expression as a Single Logarithm • Evaluate Logarithms Whose Base Is Neither 10 Nor e • Graph a Logarithmic Function Whose Base Is Neither 10 Nor e 4.2 The Graph of a Polynomial Function; Models 205 Analyze the Graph of a Polynomial Function • Build Cubic Models from Data 4.3 The Real Zeros of a Polynomial Function 214 Use the Remainder and Factor Theorems • Use Descartes’ Rule of Signs to Determine the Number of Positive and the Number of Negative Real Zeros of a Polynomial Function • Use the Rational Zeros Theorem to List the Potential Rational Zeros of a Polynomial Function • Find the Real Zeros of a Polynomial Function • Solve Polynomial Equations • Use the Theorem for Bounds on Zeros • Use the Intermediate Value Theorem 4.4 Complex Zeros; Fundamental Theorem of Algebra 229 Use the Conjugate Pairs Theorem • Find a Polynomial Function with Specified Zeros • Find the Complex Zeros of a Polynomial Function 4.5 Properties of Rational Functions 236 Find the Domain of a Rational Function • Find the Vertical Asymptotes of a Rational Function • Find the Horizontal or Oblique Asymptote of a Rational Function 4.6 The Graph of a Rational Function 247 Analyze the Graph of a Rational Function • Solve Applied Problems Involving Rational Functions 4.7 Polynomial and Rational Inequalities 259 Solve Polynomial Inequalities Graphically and Algebraically • Solve Rational Inequalities Graphically and Algebraically Chapter Review 266 Chapter Test 269 Cumulative Review 269 Chapter Project 271
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