Class Table library

  Function and Relation Library

    This set of pages is an extension of the "Function Library" in the text Exploring Functions through The Use of Manipulatives.   CONSIDER THIS MATERIAL UNDER CONSTRUCTION.

Three Most Important Functions:
identity, x
opposite, -x
reciprocal, 1/x
Lines:
vertical lines, x = a, a = some constant
horizontal lines, y = a, a = some constant
linear functions, y = ax + b, etc.
Equations of Lines, y - y1 =m (x - x1), etc.
Solving Linear Equations Graphically, Solve ax + b = cx + d
 
Ways New Functions Are Created
piece-wise defined function
composition of functions -- how functions are added, subtracted, multiplied and otherwise composed,
dilation by a constant, not just y=f(x) but y=af(x), where a is a constant,
dilation by a nonconstant function, not just y=f(x) or y=af(x), but y = g(x)f(x) and y = g(x)/f(x)
shift, not just y=f(x), y=f(x)+a or y =f(x) +g(x)
A Family of Quadratics y = ax2 + bx + c
Squaring, y = x2, y = x ·x
Square Root Functions, y = x
Roots and Exponents, x is x1/2
Polynomial Functions, y = x3, y = x ·x ·x, etc.
Rational Functions, y = 1/x3, y = 1/(x+2), etc.
Exponential or Power Functions, bx
A Bit about e
Exponential Function, exp(x) or ex
Lograthmic Functions, logb(x)
Natual Log Function, ln(x) or loge(x)
More Examples of Composite Functions:
Absolute Value Function, |x|
Conic Sections:
Circle, x2 + y2 = r2
Ellispe, x2/a2 + y2/b2 = 1
Hyperbola, x2/a2 - y2/b2 = 1
Parabolas - A Family of Quadratics y = ax2 + bx + c
Trigonometric Functions, each function
sine, sin(x)
cosecant, csc(x), 1/sin(x)
cosine, cos(x)
secant, sec(x), 1/cos(x)
tangent, tan(x), sin(x)/cos(x)
cotangent, cot(x), 1/tan(x)

    This page is from Exploring Functions Throught the Use of Manipulatives (ISBN: 0-9623593-3-5).

    You are hereby granted permission to make ONE printed copy of this page and its picture(s) for your PERSONAL and not-for-profit use. YOU MAY NOT MAKE ANY ADDITIONAL COPIES OF THIS PAGE, ITS PICTURE(S), ITS SOUND CLIP(S), OR ITS ANIMATED GIFS WITHOUT PERMISSION.


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