Intermediate Algebra: Functions and Authentic Applications

by Lehmann, Jay

• ISBN13: 9780130144980
• ISBN10: 0130144983
• Edition: 1st
• Copyright: 1999-12-01
• Publisher: PRENTICE HALL

Summary

For courses in Intermediate Algebra that incorporate a graphing calculator. Unique and enthusiastic in its approach, Lehmann's text is a rich combination of important skills, concepts, and applications. This text captivates students' and instructors' interest as they use curve fitting to model current, compelling, and authentic situations. The curve fitting approach emphasizes concepts related to functions in a natural, substantial way and encourages students to view functions graphically, numerically, and symbolically as well as to verbally describe concepts related to functions. The examples in the test demonstrate both how to perform skills and how to investigate concepts. Students learn why they perform skills to solve problems as well as how to solve the problems. Explorations deepen students' understanding as they investigate mathematics with graphing calculator and pencil and paper activities.

Table of Contents

Preface	xiii
Linear Functions	1	(48)
Using Qualitative Graphs to Describe Situations	1	(5)
Sketching Graphs of Linear Equations	6	(9)
Slope of a line	15	(8)
Graphical, Numerical, and Symbolic Significance of Slope	23	(9)
Finding Linear Equations	32	(6)
Functions	38	(11)
Taking It to the Lab	44	(1)
Chapter Summary	45	(1)
Key Points of This Chapter	45	(1)
Review Exercises	46	(2)
Chapter Test	48	(1)
Modeling with Linear Functions	49	(40)
Using Lines to Model Data	49	(8)
Finding Equations for Linear Models	57	(8)
Function Notation and Making Predictions	65	(11)
Slope is a Rate of Change	76	(13)
Taking It to the Lab	82	(4)
Chapter Summary	86	(1)
Key Points of This Chapter	86	(1)
Review Exercises	87	(1)
Chapter Test	88	(1)
Systems of Linear Equations	89	(42)
Using Graphs to Solve Systems	89	(11)
Using Elimination and Substitution to Solve Systems	100	(7)
Using Systems to Model Data	107	(8)
Using Linear Inequalities in One Variable to Make Predictions	115	(16)
Taking It to the Lab	124	(2)
Chapter Summary	126	(1)
Key Points of This Chapter	126	(1)
Review Exercises	127	(1)
Chapter Test	128	(1)
Cumulative Review of Chapters 1--3	129	(2)
Exponential Functions	131	(52)
Properties of Exponents	131	(7)
Rational Exponents	138	(10)
Sketching Graphs of Exponential Functions	148	(10)
Finding Equations for Exponential Models	158	(6)
Using Exponential Functions to Model Data	164	(19)
Taking It to the Lab	174	(4)
Chapter Summary	178	(1)
Key Points of This Chapter	178	(1)
Review Exercises	179	(2)
Chapter Test	181	(2)
Logarithmic Functions and Inverse Functions of Linear Functions	183	(42)
Finding Inverse Functions of Linear Functions	183	(9)
Logarithmic Functions	192	(8)
Properties of Logarithms	200	(5)
Using the Power Property with Exponential Models to Make Predictions	205	(8)
More Properties of Logarithms	213	(12)
Taking It to the Lab	219	(1)
Chapter Summary	220	(1)
Key Points of This Chapter	220	(1)
Review Exercises	221	(1)
Chapter Test	222	(1)
Cumulative Review of Chapters 1--5	223	(2)
Quadratic Functions	225	(46)
Sketching Graphs of Functions in Vertex Form	225	(9)
Expanding and Factoring Quadratic Expressions	234	(7)
Factoring Quadratic Expressions	241	(6)
Using Factoring to Solve Quadratic Equations	247	(11)
Sketching Graphs of Quadratic Functions in Standard Form	258	(13)
Chapter Summary	266	(1)
Key Points of This Chapter	266	(1)
Review Exercises	267	(1)
Chapter Test	268	(3)
Using Quadratic Functions to Model Data	271	(52)
Solving Quadratic Equations by Extracting Square Roots	271	(7)
Solving Quadratic Equations by Completing the Square	278	(6)
Solving Quadratic Equations by Using the Quadratic Formula	284	(8)
Solving Systems of Three Linear Equations to Find Quadratic Functions	292	(5)
Solving Systems of Three Linear Equations to Find Quadratic Models	297	(7)
Modeling with Quadratic Functions	304	(19)
Taking It to the Lab	313	(5)
Chapter Summary	318	(1)
Key Points of This Chapter	318	(1)
Review Exercises	319	(2)
Chapter Test	321	(1)
Cumulative Review of Chapters 1--7	321	(2)
Polynomials and Rational Functions	323	(62)
Factoring Sums and Differences of Cubes and Factoring by Grouping	323	(7)
Finding the Domains of Rational Functions and Simplifying Rational Expressions	330	(9)
Multiplying and Dividing Rational Expressions	339	(6)
Adding and Subtracting Rational Expressions	345	(9)
Simplifying Complex Rational Expressions	354	(5)
Solving Rational Equations	359	(7)
Modeling with Rational Functions	366	(19)
Taking It to the Lab	376	(3)
Chapter Summary	379	(1)
Key Points of This Chapter	379	(1)
Review Exercises	380	(2)
Chapter Test	382	(3)
Radical Functions	385	(48)
Simplifying Radical Expressions	385	(7)
Adding, Subtracting, and Multiplying Radical Expressions	392	(8)
Rationalizing Denominators and Simplifying Quotients of Radical Expressions	400	(6)
Sketching Graphs and Combining Square Root Functions	406	(7)
Solving Square Root Equations	413	(6)
Modeling Using Square Root Functions	419	(14)
Taking It to the Lab	427	(2)
Chapter Summary	429	(1)
Key Points of This Chapter	429	(1)
Review Exercises	430	(1)
Chapter Test	431	(2)
Modeling with Sequences and Series	433	(34)
Arithmetic Sequences	433	(8)
Geometric Sequences	441	(7)
Arithmetic Series	448	(6)
Geometric Series	454	(13)
Taking It to the Lab	459	(3)
Chapter Summary	462	(1)
Key Points of This Chapter	462	(1)
Review Exercises	462	(1)
Chapter Test	463	(1)
Cumulative Review of Chapters 1--10	464	(3)
Additional Topics	467	(46)
Absolute Value Equations and Inequalities	467	(5)
Inequalities in Two Variables	472	(7)
Natural Logarithms	479	(5)
Complex Numbers	484	(7)
Pythagorean Theorem, Distance Formula, and Circles	491	(7)
Ellipses and Hyperbolas	498	(8)
Solving Nonlinear Systems of Equations	506	(7)
A Reviewing Prerequisite Material	513	(8)
A.1 Plotting Points	513	(1)
A.2 Identifying Real Numbers	513	(1)
A.3 Performing Arithmetic with Signed Numbers	514	(1)
A.4 Constants, Variables, Expressions, and Equations	515	(1)
A.5 Using Distributive Laws	516	(1)
A.6 Combining Like Terms	516	(1)
A.7 Reviewing Order of Operations	516	(1)
A.8 Solving Linear Equations	517	(1)
A.9 Solving Literal Equations in Two Variables	518	(1)
A.10 Equivalent Expressions and Equivalent Equations	519	(2)
B Using a TI-82 or TI-83 Graphing Calculator	521	(14)
B.1 Turning Your Graphing Calculator On and Off	521	(1)
B.2 Making Your Screen Lighter or Darker	521	(1)
B.3 Entering a Function	521	(1)
B.4 Graphing a Function	522	(1)
B.5 Tracing a Function without a Scattergram	522	(1)
B.6 Zooming	522	(1)
B.7 Setting the Window Format	523	(1)
B.8 Plotting Points for a Scattergram	524	(1)
B.9 Tracing a Scattergram	524	(1)
B.10 Graphing Functions with a Scattergram	525	(1)
B.11 Tracing a Function with a Scattergram	525	(1)
B.12 Turning a Plotter ``On'' or ``Off''	525	(1)
B.13 Creating a Table	525	(1)
B.14 Creating a Table for Two Functions	526	(1)
B.15 Using ``Ask'' in a Table	526	(1)
B.16 Finding the Regression Curve for Some Data	527	(1)
B.17 Plotting Points for Two Scattergrams	528	(1)
B.18 Finding the Intersection Point(s) of Two Curves	529	(1)
B.19 Finding the Minimum or Maximum of a Curve	530	(1)
B.20 Storing a Value	530	(1)
B.21 Graphing Sequences	530	(1)
B.22 Turning a Function ``On'' or ``Off''	531	(1)
B.23 Finding Coordinates of Points	531	(1)
B.24 Graphing Functions with Axes ``Turned Off''	531	(1)
B.25 Entering a Function using Yn references	532	(1)
B.26 Responding to Error Messages	532	(3)
C Comparing TI-82/83/85/86 Calculator Commands	535	(2)
Answers to Odd-Numbered Exercises	537	(36)
Index	573