ix CONTENTS 2.5 Equations of Lines and Linear Models 253 Point-Slope Form ■ Slope-Intercept Form ■ Vertical and Horizontal Lines ■ Parallel and Perpendicular Lines ■ Modeling Data ■ Graphical Solution of Linear Equations in One Variable Summary Exercises on Graphs, Circles, Functions, and Equations 266 2.6 Graphs of Basic Functions 267 Continuity ■ The Identity, Squaring, and Cubing Functions ■ The Square Root and Cube Root Functions ■ The Absolute Value Function ■ Piecewise-Defined Functions ■ The Relation x = y 2 2.7 Graphing Techniques 279 Stretching and Shrinking ■ Reflecting ■ Symmetry ■ Even and Odd Functions ■ Translations Chapter 2 Quiz (Sections 2.5–2.7) 296 2.8 Function Operations and Composition 297 Arithmetic Operations on Functions ■ The Difference Quotient ■ Composition of Functions and Domain Test Prep 312 ■ Review Exercises 316 ■ Test 321 3 Polynomial and Rational Functions 323 3.1 Quadratic Functions and Models 324 Polynomial Functions ■ Quadratic Functions ■ Graphing Techniques ■ Completing the Square ■ The Vertex Formula ■ Quadratic Models 3.2 Synthetic Division 340 Synthetic Division ■ Remainder Theorem ■ Potential Zeros of Polynomial Functions 3.3 Zeros of Polynomial Functions 347 Factor Theorem ■ Rational Zeros Theorem ■ Number of Zeros ■ Conjugate Zeros Theorem ■ Zeros of a Polynomial Function ■ Descartes’ Rule of Signs 3.4 Polynomial Functions: Graphs, Applications, and Models 359 Graphs of ƒ1x2 = axn ■ Graphs of General Polynomial Functions ■ Behavior at Zeros ■ Turning Points and End Behavior ■ Graphing Techniques ■ Intermediate Value and Boundedness Theorems ■ Approximations of Real Zeros ■ Polynomial Models Summary Exercises on Polynomial Functions, Zeros, and Graphs 378 3.5 Rational Functions: Graphs, Applications, and Models 380 The Reciprocal Function ƒ1x 2 = 1 x ■ The Function ƒ1x 2 = 1 x 2 ■ Asymptotes ■ Graphing Techniques ■ Rational Models Chapter 3 Quiz (Sections 3.1–3.5) 401
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