Cover  cover 
Title Page  i 
Copyright Page  ii 
Dedication  iii 

An Overview and Directions  v 
Table of Contents  vii 

Essential to Every Activity  
0: Speaking, Hearing, and Writing about Functions and their Graphs  1 
01: Describe Graphs: Technical and Creative Perspectives  1 
02: The Identity Function is the Input Function  2 
03a: Describe a Graph by Creating a Wordbank  2 
03b: Supply a Wordbank to Assist in Describing the Graph of Function  3 
04: Present a "Paper"  3 
05: Play 20 Questions  4 
06: "I'm Thinking of a Function"  5 
4: Visualizing Functions and Graphs  6 
41: Draw a Function in the Air  6 
42: Doing Math "Exercises"  6 
43: Take a Limit with Your Hands  7 

Families of Functions: Translations, Reflections  
11: Addition of Functions, Vertical Slides  8 
111: Vertical Slides  8 
12: Product of Functions, Reflection about the Horizontal  11 
121: Reflections about a Horizontal Line  11 
13: Other Compositions of Functions, Horizontal Slides  13 
131: Horizontal Slides or Translations  13 
14: More Compositions of Functions, Reflections about the Vertical  15 
140: PointPlotting  15 
141: Discussing the Composition of a Function  15 
142: Reflection about a Vertical Line  17 

Solving Equations and Systems  
15: Solving Systems, Making Statements  18 
151: Using A Graph as a Boundary  18 
152: Solving An Equation Graphically  19 

An Introduction to Functions  
1: TeacherLead PointPlotting of a Function  23 
11: Examine a Function Through PointPlotting  23 
2: Student Exploration Using PointPlotting  25 
21: Discovery by Pairs of Students  25 
3: Create a Function Poster Library  28 
31: Make a Poster Library  28 

A Closer Look at Functions  
5: The Slope of a Curve at a Point  31 
51: Read Slope from the Slopemeter  31 
52: Read the Slope Using a Tangent to a Curve  33 
53: Computed Slope by the Slope Formula  34 
54: Guessing the Slope of A Function Whose Slope is Computed by Taking the Derivative  34 

6: Reflections about Y = X  36 
61: Discuss the Differences, Predict the Graph  36 
62: Simple and Mental Reflection about Y=X  37 
63: Manipulatively Finding a Reflection about Y=X  37 
64: Verification through Verbalization and Algebraic Coding  39 
65: Bounding an Area  39 
7: Inversely So: Finding the Potential Inverse Function  41 
71: The Vertical Line Test  41 
72: The Horizontal Line Test  42 
73: Using Vertical and Horizontal Lines to Ascertain Domain and Range  42 
74: Determining the Inverse Function  44 
8: Considering the Slope of Inverse Functions  47 
81: Estimating Slopes of Inverse Functions  47 
82: Generalizing about the Slopes of Functions and Their Inverses  47 
9: Function Values at Neighborhoods and Extremes  48 
91: Function Values in Neighborhoods and at Extremes  48 
92: Consider the Value of the Function in a Neighborhood about a Restricted Value  50 
93: Consider Boring Cases  51 
10: The Unit Circle  53 
101: Measurement of the Trig Functions of One Angle  53 
102: Generalizing about the Behavior of A Trig Function  54 
103: Pythagorean Identities  54 
The Unit Circle Overhead Model and Activity Sheet  56 

More on Dilation  
16: By a Constant Functions, Making Things Fat and Skinny  57 
161: Comparing Dilations  58 
162: A Project  58 
17: More Addition of Functions: Polynomials  60 
171: Addition of Functions  60 
18: More Product of Functions: Rational, Trig Functions, and Envelope Functions  63 
181: Product of Functions [Everyday Functions]  64 
182: Predicting A Graph Based on the Behavior of Related Functions  68 
183: Graphing Nonroutine functions  70 

APPENDIX 
Table of Contents  A1 
Function and Relation Library  A2 
Lines: Vertical and Horizontal lines, Linear Functions  A2 
Three Most Important Functions: Identity, Opposite, Reciprocal  A3 
Family of Quadratics, Squaring & Square Root, Polynomials, Roots and Exponents  A4 
Exponential or Power Functions, A Bit about e, the Exponential Function  A5 
Lograthmic Functions, the Natual Log Function, Absolute Value Function Conics  A6 
Conics  A7 
Trigonometric Functions and the Unit Circle, Trigonometric Functions and the Unit Circle,  A8, A9 
Mechanical Manipulatives: Demo Pack and Unit Circle Assembly and Masters  A10  A14 
Parent Function Masters: Shapes for 1/x, (1  x²), (4  x²), (9  x²),  A15 
halfplane, sine or cosine, not x, x, exp(x) or ln(x), x, ¦x¦, x², and x  A16  A19 
Additional Function Masters: Shapes for secant or cosecant, tangent or  A20 
cotangent, .25x², .5x², 2x², 4x², 10x², .1x², x² and not x², y>x², and y < x²,  A21 A24 
not 2x², not 4x², not 10x², and not .1x², not .25x² and not .5x²  A25  A26 
Coordinate Planes: Coordinate Plane Paper, 2 Planes Paper, 4 Planes Paper  A27  A29 
About the Author  A30 

Additional Planes  Planes
