Contents
Preface
Chapter 1 Functions
Prerequisite Skills
2
1.1 Functions, Domain, and Range
4
1.2 Functions and Function Notation
16
1.3 Maximum or Minimum of a Quadratic
Function
25
Use Technology Use a TI-Nspire™™ CAS
Graphing Calculator to Find Maximum
or Minimum and the Zeros of a
Quadratic Function
33
1.4 Skills You Need: Working With
Radicals
34
Use Technology Use a TI-Nspire™ CAS
Graphing Calculator to Explore
Operations With Radicals
41
43
1.5 Solve Quadratic Equations
1.6 Determine a Quadratic Equation
Given its Roots
52
1.7 Solve Linear-Quadratic Systems
60
Chapter 1 Review
70
72
74
Chapter 1 Practice Test
Task: Laser Beams
2.7 Inverse of a Function
132
Chapter 2 Review
142
Chapter 2 Practice Test
144
Task: Functions in Design
146
Chapter 3 Exponential Functions 147
Prerequisite Skills
148
3.1 The Nature of Exponential Growth
150
Use Technology Use Lists and Trace Features
on a TI-Nspire™ CAS Graphing
Calculator
158
3.2 Exponential Decay: Connecting to
Negative Exponents
160
3.3 Rational Exponents
170
3.4 Properties of Exponential Functions 178
3.5 Transformations of
Exponential Functions
188
3.6 Making Connections: Tools and
Strategies for Applying Exponential
Models
199
Chapter 3 Review
210
212
214
218
Chapter 3 Practice Test
Chapters 1 to 3 Review
Task: Radioactive Isotopes
Functions
75
Chapter 4 Trigonometry
219
Prerequisite Skills
2.1 Functions and Equivalent Algebraic
Expressions
76
Prerequisite Skills
4.1 Special Angles
220
222
78
Use Technology Use The Geometer's
IV NEL • Functions 11 • Contents
4.2 Co-terminal and Related Angles
Use Technology Use a Computer Algebra
TI-Nspire™ CAS Graphing Calculator 86
2.2 Skills You Need: Operations With
Rational Expressions
88
2.3 Horizontal and Vertical Translations
of Functions
97
2.4 Reflections of Functions
105
2.5 Stretches of Functions
113
Sketchpad® to Explore
Transformations
2.6 Combinations of Transformations
Ch
Tas
Cha
Prereq
6.1 Se
Chapter 2 Transformations of
Use Technology Graph Functions Using a
Cl
System to Find Exact Trigonometric
Ratios and Angles
241
4.3 Reciprocal Trigonometric Ratios
243
4.4 Problems in Two Dimensions
249
Use Technology Use Geometry Software to
Test for the Ambiguous Case
4.5 Problems in Three Dimensions
4.6 Trigonometric Identities
123
125
232
Chapter 4 Review
Chapter 4 Practice Test
Task: Pyramids and Angles of Elevation
259
261
270
276
278
280
Use Tec
Gra
in a
6.2 Recu
6.3 Pasca
Binon
6.4 Arithn
6.5 Geomet
6.6 Arithme
6.7 Geometri
Chapter 6 Revi
Chapter 6 Practi
Task: Mathemati
Chapter 5 Trigonometric Functions 281
Prerequisite Skills
5.1 Modelling Periodic Behaviour
5.2 The Sine Function and the Cosine
Function
Use Technology Dynamically Unwrap the
Unit Circle
5.3 Investigate Transformations of Sine
and Cosine Functions
5.4 Graphing and Modelling with
y = asin[k(x - d)] + c and
y = acos|k(x - d)] + c
5.5 Data Collecting and Modelling
5.6 Use Sinusoidal Functions to Model
Periodic Phenomena Not Involving
Angles
282
284
294
302-
304
313
322
333
Use Technology Create a Scatter Plot and
a Function Using a TI-Nspire™ CAS
Graphing Calculator
343
Chapter 5 Review
344
Chapter 5 Practice Test
346
Chapters 4 and 5 Review
Task: Modelling a Rotating Object
348
350
Chapter 6 Discrete Functions
351
Prerequisite Skills
352
354
6.1 Sequences as Discrete Functions
Chapter 7 Financial Applications
Prerequisite Skills
7.1. Simple Interest
7.2 Compound Interest
7.3 Present Value
415
416
418
426
436
7,4 Annuities
7.5 Present Value of an Annuity
Chapter 7 Review
Chapter 7 Practice Test
Chapters 6 and 7 Review
Task: Loans and Annuities Due
444
456
464
466
468
470
Course Review
471
Prerequisite Skills Appendix
Technology Appendix
Answers
478
496
Glossary
Index
Credits
517
587
595
600
Use Technology Use a TI-NspireT™ CAS
Graphing Calculator to Write Terms
in a Sequence
6.2 Recursive Procedures
6.3 Pascal's Triangle and Expanding
Binomial Powers
6.4 Arithmetic Sequences
6.5 Geometric Sequences
6.6 Arithmetic Series
6.7 Geometric Series
Chapter 6 Review
Chapter 6 Practice Test
Task: Mathematics in Media Studies
364
365
373
380
388
395
402
410
412
414
Contents • NEL V