Modeling, Functions, and Graphs Algebra for College Students (with iLrn™ Printed Access Card)

by Yoshiwara, Katherine; Yoshiwara, Bruce

• ISBN13: 9780534419417
• ISBN10: 0534419410
• Edition: 4th
• Format: Hardcover
• Copyright: 2006-08-25
• Publisher: Cengage Learning

Summary

The Fourth Edition of Yoshiwara and Yoshiwara's MODELING, FUNCTIONS, AND GRAPHS: ALGEBRA FOR COLLEGE STUDENTS includes content found in a typical algebra course, along with introductions to curve-fitting and display of data. Yoshiwara and Yoshiwara focus on three core themes throughout their textbook: Modeling, Functions, and Graphs. In their work of modeling and functions, the authors utilize the Rule of Four, which is that all problems should be considered using algebraic, numerical, graphical, and verbal methods. The authors motivate students to acquire the skills and techniques of algebra by placing them in the context of simple applications that use real-life data.

Table of Contents

Functions and Their Graphs	1	(122)
Investigation 1 Sales on Commission	2	(1)
Linear Models	3	(16)
Tables, Graphs, and Equations	3	(2)
Choosing Scales for the Axes	5	(2)
Linear Equations	7	(2)
Intercepts	9	(1)
Intercept Method for Graphing Lines	10	(9)
Functions	19	(20)
Definition of Function	19	(1)
Functions Defined by Tables	20	(1)
Functions Defined by Graphs	21	(2)
Functions Defined by Equations	23	(1)
Function Notation	24	(1)
Evaluating a Function	25	(2)
Operations with Function Notation	27	(12)
Graphs of Functions	39	(17)
Reading Function Values from a Graph	39	(2)
Constructing the Graph of a Function	41	(1)
The Vertical Line Test	42	(2)
Graphical Solution of Equations and Inequalities	44	(12)
Slope and Rate of Change	56	(21)
Using Ratios for Comparison	56	(1)
Measuring Steepness	57	(1)
Definition of Slope	58	(1)
Notation for Slope	59	(2)
Lines Have Constant Slope	61	(1)
Meaning of Slope	62	(1)
A Formula for Slope	63	(14)
Linear Functions	77	(15)
Slope-Intercept Form	77	(2)
Slope-Intercept Method of Graphing	79	(1)
Finding a Linear Equation from a Graph	80	(1)
Point-Slope Form	81	(11)
Linear Regression	92	(31)
Fitting a Line through Two Points	92	(1)
Scatterplots	93	(2)
Linear Regression	95	(2)
Linear Interpolation and Extrapolation	97	(14)
Summary and Review	111	(9)
Projects for Chapter 1	120	(3)
Modeling with Functions	123	(110)
Investigation 2 Epidemics	124	(1)
Investigations 3 Perimeter and Area	125	(1)
Nonlinear Models	126	(13)
Solving Nonlinear Equations	126	(2)
Solving Formulas	128	(1)
More Extraction of Roots	128	(1)
Compound Interest and Inflation	129	(1)
Other Nonlinear Equations	130	(9)
Some Basic Functions	139	(15)
Absolute Value	139	(2)
Examples of Models	141	(1)
Investigation 4 Eight Basic Functions	142	(2)
Graphs of Eight Basic Functions	144	(1)
Properties of the Basic Functions	144	(2)
Functions Defined Piecewise	146	(8)
Transformations of Graphs	154	(21)
Vertical Translations	154	(2)
Horizontal Translations	156	(3)
Scale Factors	159	(16)
Functions as Mathematical Models	175	(17)
The Shape of the Graph	175	(3)
Using the Basic Functions as Models	178	(2)
Modeling with Piecewise Functions	180	(12)
The Absolute Value Function	192	(11)
Absolute Value Equations	193	(2)
Absolute Value Inequalities	195	(1)
Using the Absolute Value in Modeling	196	(2)
Measurement Error	198	(5)
Domain and Range	203	(30)
Definitions of Domain and Range	203	(1)
Finding Domain and Range from a Graph	204	(3)
Finding the Domain from a Formula	207	(1)
Restricting the Domain	208	(7)
Summary and Review	215	(9)
Projects for Chapter 2	224	(9)
Power Functions	233	(88)
Investigation 5 Inflating a Balloon	234	(1)
Variation	235	(20)
Direct Variation	235	(2)
The Scaling Property of Direct Variation	237	(2)
Finding a Formula for Direct Variation	239	(1)
Direct Variation with a Power of x	240	(1)
Scaling	241	(1)
Inverse Variation	242	(2)
Finding a Formula for Inverse Variation	244	(11)
Integer Exponents	255	(13)
Negative Exponents	255	(2)
Power Functions	257	(3)
Working with Negative Exponents	260	(1)
Laws of Exponents	260	(8)
Roots and Radicals	268	(14)
nth Roots	268	(1)
Exponential Notation for Radicals	268	(2)
Irrational Numbers	270	(1)
Using Fractional Exponents to Solve Equations	271	(1)
Power Functions	272	(1)
Solving Radical Equations	273	(2)
A Note on Roots of Negative Numbers	275	(7)
Rational Exponents	282	(15)
Powers of the Form am/n	282	(1)
Power Functions	283	(1)
More About Scaling	284	(1)
Radical Notation	285	(1)
Operations with Rational Exponents	286	(1)
Solving Equations	287	(1)
Investigation 6 Vampire Bats	287	(10)
Joint Variation	297	(24)
Functions of Two or More Variables	297	(1)
Tables of Values	298	(1)
Joint Variation	299	(3)
Graphs	302	(9)
Summary and Review	311	(7)
Projects for Chapter 3	318	(3)
Exponential Functions	321	(80)
Investigation 7 Population Growth	322	(1)
Exponential Growth and Decay	323	(17)
Exponential Growth	323	(1)
Growth Factors	324	(1)
Percent Increase	325	(3)
Exponential Decay	328	(1)
Investigation 8 Exponential Decay	328	(1)
Decay Factors	329	(2)
Comparing Linear Growth and Exponential Growth	331	(9)
Exponential Functions	340	(15)
Graphs of Exponential Functions	340	(2)
Transformations of Exponential Functions	342	(1)
Comparing Exponential and Power Functions	343	(1)
Exponential Equations	344	(2)
Graphical Solution of Exponential Equations	346	(9)
Logarithms	355	(10)
Using the Conversion Equations	357	(1)
Approximating Logarithms	357	(2)
Base 10 Logarithms	359	(1)
Solving Exponential Equations	359	(2)
Application to Exponential Models	361	(4)
Properties of Logarithms	365	(11)
Using the Properties of Logarithms	366	(1)
Solving Exponential Equations	367	(2)
Applications	369	(1)
Compound Interest	370	(1)
Solving Formulas	371	(5)
Exponential Models	376	(25)
Fitting an Exponential Function through Two Points	376	(2)
Doubling Time	378	(3)
Half-Life	381	(1)
Annuities and Amortization	382	(9)
Summary and Review	391	(6)
Projects for Chapter 4	397	(4)
Logarithmic Functions	401	(74)
Inverse Functions	402	(19)
Finding a Formula for the Inverse Function	403	(1)
Inverse Function Notation	404	(2)
Graph of the Inverse Function	406	(1)
When Is the Inverse a Function?	407	(2)
Mathematical Properties of the Inverse Function	409	(1)
Symmetry	410	(2)
Domain and Range	412	(9)
Logarithmic Functions	421	(16)
Inverse of the Exponential Function	421	(3)
Graphs of Logarithmic Functions	424	(2)
Evaluating Logarithmic Functions	426	(1)
Logarithmic Equations	426	(2)
Using the Properties of Logarithms	428	(7)
Investigation 9 Interest Compounded Continuously	435	(2)
The Natural Base	437	(14)
The Natural Exponential Function	437	(1)
The Natural Logarithmic Function	438	(1)
Properties of the Natural Logarithm	439	(1)
Solving Equations	440	(1)
Exponential Growth and Decay	441	(2)
Continuous Compounding	443	(8)
Logarithmic Scales	451	(24)
Using Log Scales	453	(1)
Equal Increments on a Log Scale	454	(2)
Acidity and the pH Scale	456	(2)
Decibels	458	(1)
The Richter Scale	459	(7)
Summary and Review	466	(6)
Projects for Chapter 5	472	(3)
Quadratic Functions	475	(86)
Investigation 10 Height of a Baseball	476	(1)
Factors and x-Intercepts	477	(12)
Zero-Factor Principle	477	(1)
Solving Quadratic Equations by Factoring	478	(3)
Applications	481	(1)
Solutions of Quadratic Equations	481	(1)
Equations Quadratic in Form	482	(7)
Solving Quadratic Equations	489	(12)
Squares of Binomials	489	(2)
Solving Quadratic Equations by Completing the Square	491	(2)
The General Case	493	(2)
Quadratic Formula	495	(1)
Applications	496	(5)
Graphing Parabolas	501	(14)
The Graph of y = ax2	501	(1)
The Graph of y = x2 + c	502	(1)
The Graph of y = ax2 + bx	503	(1)
Finding the Vertex	504	(1)
The Graph of y = ax2 + bx + c	505	(1)
Number of x-Intercepts	506	(1)
Sketching a Parabola	507	(8)
Problem Solving	515	(13)
Investigation 11 Revenue from Theater Tickets	515	(1)
Maximum or Minimum Values	516	(1)
The Vertex Form for a Parabola	517	(2)
Graphing with the Vertex Form	519	(1)
Systems Involving Quadratic Equations	519	(9)
Quadratic Inequalities	528	(10)
Solving Inequalities Graphically	528	(3)
Solving Quadratic Inequalities Algebraically	531	(7)
Curve Fitting	538	(23)
Finding a Quadratic Function through Three Points	539	(3)
Finding an Equation in Vertex Form	542	(10)
Summary and Review	552	(6)
Projects for Chapter 6	558	(3)
Polynomial and Rational Functions	561	(76)
Investigations 12 Bezier Curves	562	(3)
Polynomial Functions	565	(12)
Products of Polynomials	566	(1)
Special Products	567	(1)
Factoring Cubics	568	(1)
Modeling with Polynomials	569	(8)
Graphing Polynomial Functions	577	(11)
Classifying Polynomials by Degree	577	(1)
Cubic Polynomials	578	(1)
Quartic Polynomials	579	(1)
x-Intercepts and the Factor Theorem	580	(2)
Zeros of Multiplicity Two or Three	582	(6)
Complex Numbers	588	(12)
Imaginary Numbers	588	(1)
Complex Numbers	589	(1)
Arithmetic of Complex Numbers	590	(1)
Products of Complex Numbers	591	(1)
Quotients of Complex Numbers	592	(1)
Zeros of Polynomials	593	(2)
Graphing Complex Numbers	595	(5)
Graphing Rational Functions	600	(17)
Domain of a Rational Function	603	(1)
Vertical Asymptotes	604	(2)
Horizontal Asymptotes	606	(2)
Applications	608	(9)
Equations That Include Algebraic Fractions	617	(20)
Solving Equations with Fractions Algebraically	618	(1)
Solving Equations with Fractions Graphically	619	(1)
Extraneous Solutions	619	(2)
Formulas	621	(6)
Summary and Review	627	(6)
Projects for Chapter 7	633	(4)
Linear Systems	637	(70)
Investigation 13 Interpolating Polynomials	638	(1)
Systems of Linear Equations in Two Variables	639	(15)
Solving Systems by Graphing	639	(4)
Inconsistent and Dependent Systems	643	(3)
Applications	646	(2)
An Application from Economics	648	(6)
Systems of Linear Equations in Three Variables	654	(12)
3 X 3 Linear Systems	654	(2)
Back-Substitution	656	(1)
Gaussian Reduction	657	(3)
Inconsistent and Dependent Systems	660	(1)
Applications	661	(5)
Solving Linear Systems Using Matrices	666	(16)
Coefficient Matrix and Augmented Matrix of a System	667	(1)
Elementary Row Operations	667	(3)
Matrix Reduction	670	(1)
Reducing a 3 X 3 Matrix	671	(2)
Solving Larger Systems	673	(7)
Investigation 14 Input-Output Models	680	(2)
Linear Inequalities	682	(8)
Graphs of Inequalities in Two Variables	682	(1)
Linear Inequalities	683	(1)
Using a Test Point	684	(2)
Systems of Inequalities	686	(4)
Linear Programming	690	(17)
The Objective Function and Constraints	690	(1)
Feasible Solutions	691	(1)
The Optimum Solution	692	(8)
Summary and Review	700	(5)
Projects for Chapter 8	705	(2)
APPENDIX A Algebra Skills Refresher	707	(90)
Numbers and Operations	707	(6)
Order of Operations	707	(1)
Parentheses and Fraction Bars	707	(1)
Radicals	708	(1)
Scientific Notation	709	(4)
Linear Equations and Inequalities	713	(7)
Solving Linear Equations	713	(2)
Formulas	715	(1)
Linear Inequalities	716	(1)
Interval Notation	717	(3)
Algebraic Expressions and Problem Solving	720	(9)
Problem Solving	722	(1)
Supply and Demand	722	(1)
Percent Problems	723	(1)
Weighted Averages	724	(5)
Graphs and Equations	729	(7)
Reading a Graph	729	(1)
Graphs of Equations	730	(6)
Linear Systems in Two Variables	736	(7)
Solving Systems by Substitution	736	(1)
Solving Systems by Elimination	737	(6)
Laws of Exponents	743	(6)
Product of Powers	743	(1)
Quotients of Powers	744	(1)
Power of a Power	745	(1)
Power of a Product	746	(1)
Power of a Quotient	746	(3)
Polynomials and Factoring	749	(7)
Polynomials	749	(1)
Products of Polynomials	750	(1)
Products of Binomials	751	(1)
Factoring	751	(1)
Common Factors	751	(1)
Opposite of a Binomial	752	(1)
Polynomial Division	752	(4)
Factoring Quadratic Trinomials	756	(5)
Special Products and Factors	758	(3)
Working with Algebraic Fractions	761	(12)
Reducing Fractions	761	(2)
Products of Fractions	763	(1)
Quotients of Fractions	764	(1)
Sums and Differences of Like Fractions	764	(1)
Lowest Common Denominator	765	(1)
Building Fractions	766	(1)
Sums and Differences of Unlike Fractions	766	(2)
Complex Fractions	768	(1)
Negative Exponents	769	(4)
Working with Radicals	773	(9)
Properties of Radicals	773	(1)
Simplifying Radicals	773	(2)
Sums and Differences of Radicals	775	(1)
Products of Radicals	775	(1)
Rationalizing the Denominator	776	(1)
Simplifying n√an	777	(1)
Extraneous Solutions to Radical Equations	778	(1)
Equations with More than One Radical	779	(3)
Facts from Geometry	782	(10)
Right Triangles and the Pythagorean Theorem	782	(1)
Isosceles and Equilateral Triangles	783	(1)
The Triangle Inequality	783	(1)
Similar Triangles	784	(1)
Volume and Surface Area	785	(1)
The Distance Formula	786	(1)
The Midpoint Formula	787	(1)
Circles	788	(4)
The Real Number System	792	(5)
Subsets of the Real Numbers	792	(1)
Rational Numbers	793	(1)
Irrational Numbers	793	(1)
Properties of the Real Numbers	794	(1)
Order Properties of the Real Numbers	795	(2)
APPENDIX B Using a Graphing Calculator	797	(12)
Getting Started	797	(1)
On and Off	797	(1)
Numbers and Operations	797	(1)
Clear and Delete	798	(1)
Entering Expressions	798	(3)
Parentheses	798	(1)
Exponents and Powers	799	(1)
Roots	799	(1)
Absolute Value	800	(1)
Scientific Notation	801	(1)
Editing Expressions	801	(1)
Overwriting	801	(1)
Recalling an Entry	801	(1)
Inserting a Character	802	(1)
Recalling an Answer	802	(1)
Graphing an Equation	802	(3)
Standard Window	802	(1)
Tracing	803	(1)
Multiple Graphs	803	(1)
Setting the Window	803	(1)
Intersect Feature	804	(1)
Other Windows	804	(1)
Making a Table	805	(1)
Using the Auto Option	805	(1)
Using the Ask Option	805	(1)
Regression	806	(1)
Making a Scatterplot	806	(1)
Finding a Regression Equation	806	(1)
Graphing the Regression Equation	807	(1)
Function Notation and Transformations of Graphs	807	(2)
Function Notation	807	(1)
Transformation of Graphs	808	(1)
Glossary	809	(10)
Bibliography	819
Answers to Odd-Numbered Problems	1	(1)
Index	1