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# Intermediate Algebra: Functions and Authentic Applications

by
Edition:
1st
ISBN13:

ISBN10:
0130144983
Pub. Date:
12/1/1999
Publisher(s):
PRENTICE HALL

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## 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.

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)
225(46)
 Sketching Graphs of Functions in Vertex Form
225(9)
234(7)
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)
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)
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)
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)
385(48)
385(7)
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)
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)