 Complete Description of Proposed Session

 The audience will use manipulatives to graph f(x), parent functions.
The audience will given f(x), consider:
 f(x) + k,
 f(x  h),
 f(x),
 f(x),
 f(x  h) + k,
 f(y),
 1/f(x), and
 f^{1}(x).
 Describe a function.
 Compare input to output.
 Compare two functions.
 Generalize about a
family of expressions.
 Solve traditional and nontraditional equations
and systems (as a end in itself and as a precursor to calculator or computer solution).
 Examine functions of the form y = a(x)f(x), power, rational, and
envelope functions.
 Consider the implications and
manipulative/concrete
presentation techniques.
 Introduction
 Manipulatives for Function Exploration:
Slopemeter, Isolator, Absolute Value Dilator
 The Possibilities with Concrete Thought

 A Closer Look at Functions
 Speaking, Hearing, and Writing about Functions and their Graphs
 Visualizing Functions and Graphs
 The Slope
 of Curves,
 of a Curve at a Point  Reflections on Y = X
 Inversely So: Finding the Potential Inverse Functions
 Considering the Slope of Inverse Functions
 Solving Systems

 Families of Functions: Translations, Reflections
 Parent Functions:
x, x, 1/x,
x, x^{2},
x, exp(x), ln(x), sin(x), cos(x), tan(x),
 Early Examples of the Addition of Functions: y = f(x) + k
 Early Examples of the Product of Functions: y = af(x)
 Early Examples of the Composition of Functions: y = g(f(x))
 More on the Composition of Functions: y = g(f(x))

 Summation
 Math Exercises
 Food for Thought:Dilation
Why does a cubic look like a cubic?
Why does the tangent function behave the way it does?
The Unit Circle Manipulatively
Why does a rational function look have the properties it has?
Dilation by a Constant Functions: y = af(x)
More on the Addition of Functions: y = f(x) + g(x)
More on the Product of Functions: y = a(x)f(x)
 Rules of Manipulative Use
 Strategies for Change
