Concepts in Algebra

by Fey, James T.; Heid, M. Kathleen

• ISBN13: 9781570397004
• ISBN10: 1570397007
• Format: Hardcover
• Copyright: 1999-01-01
• Publisher: Glencoe/McGraw-Hill School Pub

Table of Contents

Preface	xi
Acknowledgements	xv
To the Student	xvii
Variables and Functions	1	(64)
Modeling ... With Mathematics	1	(6)
Exploration I	2	(1)
Exploration II	3	(1)
Making Connections	4	(3)
Variables Related by Data in Tables	7	(6)
Exploration	9	(4)
Variables Related by Data in Graphs	13	(14)
Exploration I Constructing Graphs	15	(5)
Exploration II Interpreting Graphs	20	(7)
Variables Related by Rules	27	(8)
Exploration	29	(6)
Rules Relating Variables-Symbolic Form	35	(5)
Exploration I	36	(4)
Exploration II (Optional)	40	(1)
Order of Operations	40	(9)
Exploration I	43	(1)
Exploration II	44	(5)
Building Models of Mathematical Relations	49	(8)
Exploration I Smoothing Data in Search of Models	36	(18)
Exploration II A Small Group Experiment	54	(3)
Summary	57	(8)
Review Exercises	58	(7)
Functions and Computing Technology	65	(52)
Functions with Rules - By Hand	66	(6)
Exploration	69	(3)
Functions with Rules - Using Calculator Functions	72	(5)
Exploration	73	(3)
Making Connections	76	(1)
Functions with Rules - Using Programmable Tools	77	(6)
Exploration	79	(3)
Making Connections	82	(1)
Programs and Function Tables	83	(9)
Exploration I	85	(3)
Exploration II	88	(1)
Exploration III	89	(1)
Making Connections	90	(2)
Technology and Function Graphs	92	(14)
Graphing Tools	94	(2)
Exploration I	96	(4)
The Effects of Scales on Graphs	100	(2)
Exploration II	102	(1)
Making Connections	103	(1)
Exploration III	104	(1)
Making Connections	105	(1)
Solving Equations with Technology	106	(5)
Exploration	108	(3)
Making Connections	111	(1)
Summary	111	(6)
Review Exercises	112	(5)
Linear Functions	117	(70)
Properties of Linear Functions	117	(9)
Exploration	119	(6)
Making Connections	125	(1)
Finding and Using Linear Function Rules	126	(10)
Finding Linear Function Rules	126	(2)
Exploration I	128	(2)
Using Linear Function Rules to Analyze Situations	130	(2)
Exploration II	132	(4)
Tables of Linear Functions	136	(7)
Exploration	140	(3)
Graphs of Linear Functions	143	(15)
Exploration I	147	(3)
Making Connections	150	(4)
Exploration II	154	(1)
Making Connections	154	(3)
Making Connections	157	(1)
Solving Equations and Inequalities	158	(7)
Exploration	162	(3)
Linear Patterns in Data	165	(18)
Linear Function Rules to Model Data Patterns	166	(2)
Exploration	168	(8)
Making Connections	176	(1)
Evaluating the Goodness of Fit for a Model	176	(4)
Exploration	180	(3)
Summary	183	(4)
Review Exercises	184	(3)
Quadratic Functions	187	(48)
Recognizing Quadratic Functions	187	(9)
Exploration I	188	(3)
Exploration II	191	(2)
Making Connections	193	(3)
Properties of Quadratic Functions	196	(12)
Exploration	197	(1)
Experiment Series 1: The Effect of a in ax2 + bx + c	197	(3)
Making Connections	200	(1)
Making Connections	201	(1)
Experiment Series 2: The Effect of c in ax2 + bx + c	202	(1)
Making Connections	203	(1)
Experiment Series 3: The Effect of b in ax2 + bx + c	203	(5)
Solving Quadratic Equations and Inequalities	208	(8)
Exploration I	209	(2)
Making Connections	211	(2)
Exploration II	213	(3)
Applying Quadratic Functions	216	(8)
Exploration I	217	(2)
Exploration II	219	(5)
Polynomial Functions of Degree Greater Than Two	224	(3)
Exploration	225	(1)
Making Connections	225	(1)
Making Connections	226	(1)
Summary	227	(8)
Review Exercises	228	(2)
Review Project	230	(5)
Exponential Functions	235	(44)
Recognizing Exponential Functions	236	(16)
Exploration I	239	(4)
Exploration II	243	(3)
Exploration III	246	(2)
Making Connections	248	(4)
Properties of Exponential Functions	252	(14)
Exploration I Evaluating ax for x Between Integers	256	(3)
Exploration II Properties of Tables and Graphs for f(x) = Cax	259	(4)
Making Connections	263	(3)
Making Connections	266	(1)
Applying Exponential Functions	266	(8)
Summary	274	(5)
Review Exercises	275	(4)
Rational Functions	279	(40)
Recognizing Rational Functions	279	(10)
Exploration I	280	(2)
Exploration II	282	(2)
Making Connections	284	(1)
Exploration III	285	(1)
Making Connections	286	(3)
Properties of Rational Functions	289	(14)
Exploration I	290	(4)
Making Connections	294	(1)
Exploration II	295	(3)
Exploration III	298	(3)
Making Connections	301	(1)
Exploration IV Making Connections	302	(1)
Finding and Applying Rational Function Models	303	(9)
Exploration I	303	(2)
Exploration II	305	(2)
Exploration III	307	(5)
Summary	312	(7)
Review Exercises	313	(6)
Systems of Functions and Equations	319	(66)
Thinking About Systems	320	(5)
Exploration	320	(5)
Algebraic Models of Systems	325	(8)
Exploration I	326	(4)
Exploration II	330	(3)
Properties of Systems of Functions	333	(5)
Exploration	334	(3)
Making Connections	337	(1)
Functions with Several Input Variables	338	(6)
Exploration I	338	(2)
Exploration II	340	(1)
Exploration III	341	(3)
Equations with Several Variables	344	(11)
Exploration I	346	(5)
Making Connections	351	(1)
Exploration II	351	(1)
Exploration III	352	(3)
Systems of Equations	355	(10)
Exploration I	355	(3)
Exploration II	358	(7)
Properties of Systems of Equations	365	(6)
Exploration I	365	(4)
Exploration II	369
Making Connections	358	(13)
Linear Inequalities	371	(8)
Exploration I	371	(3)
Exploration II	374	(1)
Exploration III	375	(1)
Making Connections	376	(3)
Summary	379	(6)
Review Exercises	380	(5)
Symbolic Reasoning: Equivalent Expressions	385	(70)
Equivalent Expressions	386	(12)
Exploration I	389	(2)
Exploration II	391	(2)
Exploration III	393	(1)
Making Connections	394	(4)
Making Connections	398	(1)
Formal Symbolic Reasoning in Algebra	398	(16)
Properties of Operations	399	(13)
Exploration	412
Using Properties to Find Equivalent Expressions	406	(8)
Equivalent Linear Expressions	414	(9)
Exploration	417	(3)
Making Connections	420	(3)
Quadratics in Equivalent Forms	423	(8)
Factoring Quadratics	424	(1)
ExplorationI	425	(1)
Making Connections	426	(1)
Exploration II	426	(3)
Simplifying Quadratic Expressions	429	(1)
Exploration III	430	(1)
Rules for Simplifying Expressions	431	(12)
Equivalent Rational Expressions	435	(3)
Exploration I	438	(5)
Exploration II	443	(4)
Summary	447	(8)
Review Exercises	448	(7)
Symbolic Reasoning: Equations and Inequalities	455	(58)
Equivalent Equations	456	(7)
Exploration	458	(3)
Making Connections	461	(2)
Procedures that Produce Equivalent Equations	463	(11)
Addition Property of Equations	463	(4)
Exploration I	467	(1)
Multiplication Property of Equations	468	(1)
Exploration II	469	(2)
Making Connections	471	(2)
Substitution Property of Equations	473	(1)
Exploration III	473	(1)
Applying Properties of Equations	474	(7)
Exploration	478	(3)
Making Connections	481	(1)
Solving Equations ... Beyond the Linear Case	481	(6)
Exploration	485	(2)
Equivalent Inequalities	487	(5)
Graphs of Equivalent Inequalities	487	(3)
Exploration I	490	(1)
Making Connections	491	(1)
Transformations that Produce Equivalent Inequalities	492	(14)
Exploration II	496	(3)
Exploration III	499	(3)
Making Connections	502	(1)
Using Addition and Multiplication Properties to Solve Inequalities	503	(3)
Summary	506	(7)
Review Exercises	507	(6)
Index	513