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
    0-1: Describe Graphs: Technical and Creative Perspectives 1
    0-2: The Identity Function is the Input Function 2
    0-3a: Describe a Graph by Creating a Wordbank 2
    0-3b: Supply a Wordbank to Assist in Describing the Graph of Function 3
    0-4: Present a "Paper" 3
    0-5: Play 20 Questions 4
    0-6: "I'm Thinking of a Function" 5
4: Visualizing Functions and Graphs 6
    4-1: Draw a Function in the Air 6
    4-2: Doing Math "Exercises" 6
    4-3: Take a Limit with Your Hands 7
Families of Functions: Translations, Reflections
11: Addition of Functions, Vertical Slides 8
    11-1: Vertical Slides 8
12: Product of Functions, Reflection about the Horizontal 11
    12-1: Reflections about a Horizontal Line 11
13: Other Compositions of Functions, Horizontal Slides 13
    13-1: Horizontal Slides or Translations 13
14: More Compositions of Functions, Reflections about the Vertical 15
    14-0: Point-Plotting 15
    14-1: Discussing the Composition of a Function 15
    14-2: Reflection about a Vertical Line 17
Solving Equations and Systems
15: Solving Systems, Making Statements 18
    15-1: Using A Graph as a Boundary 18
    15-2: Solving An Equation Graphically 19
An Introduction to Functions
1: Teacher-Lead Point-Plotting of a Function 23
    1-1: Examine a Function Through Point-Plotting 23
2: Student Exploration Using Point-Plotting 25
    2-1: Discovery by Pairs of Students 25
3: Create a Function Poster Library 28
    3-1: Make a Poster Library 28
A Closer Look at Functions
5: The Slope of a Curve at a Point 31
    5-1: Read Slope from the Slopemeter 31
    5-2: Read the Slope Using a Tangent to a Curve 33
    5-3: Computed Slope by the Slope Formula 34
    5-4: Guessing the Slope of A Function Whose Slope is Computed by Taking the Derivative 34
6: Reflections about Y = X 36
    6-1: Discuss the Differences, Predict the Graph 36
    6-2: Simple and Mental Reflection about Y=X 37
    6-3: Manipulatively Finding a Reflection about Y=X 37
    6-4: Verification through Verbalization and Algebraic Coding 39
    6-5: Bounding an Area 39
7: Inversely So: Finding the Potential Inverse Function 41
    7-1: The Vertical Line Test 41
    7-2: The Horizontal Line Test 42
    7-3: Using Vertical and Horizontal Lines to Ascertain Domain and Range 42
    7-4: Determining the Inverse Function 44
8: Considering the Slope of Inverse Functions 47
    8-1: Estimating Slopes of Inverse Functions 47
    8-2: Generalizing about the Slopes of Functions and Their Inverses 47
9: Function Values at Neighborhoods and Extremes 48
    9-1: Function Values in Neighborhoods and at Extremes 48
    9-2: Consider the Value of the Function in a Neighborhood about a Restricted Value 50
    9-3: Consider Boring Cases 51
10: The Unit Circle 53
    10-1: Measurement of the Trig Functions of One Angle 53
    10-2: Generalizing about the Behavior of A Trig Function 54
    10-3: 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
    16-1: Comparing Dilations 58
    16-2: A Project 58
17: More Addition of Functions: Polynomials 60
    17-1: Addition of Functions 60
18: More Product of Functions: Rational, Trig Functions, and Envelope Functions 63
    18-1: Product of Functions [Everyday Functions] 64
    18-2: Predicting A Graph Based on the Behavior of Related Functions 68
    18-3: Graphing Nonroutine functions 70
Table of Contents A-1
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

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