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
- 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
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)
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 =
- 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.
© 2008, Agnes Azzolino