a. Families of Functions [& Relations]

At least one of the applets on this page leads to applets that were written for the Wolfram Demonstration Project. In order to run them you will need to download the Wolfram CDF reader [available FREE at http://www.wolfram.com/education/] Please read the essay on this web site entitled "Developing Function Sense" Algebra in the middle and secondary grades is largely the mathematics of function. The topic of Functions is not normally taught early in a student’s algebra career. When the topic of functions is finally taught, it is taught with emphasis on the symbolic representations of functions. Research has shown that approaching algebra from the outset through the study of functions using both symbolic and graphical representations simultaneously and in parallel is a pedagogically powerful teaching and learning strategy. Many people learn better and develop deeper understanding and intuitions about a subject if visual representations of aspects of the subject are prominent in the teaching and learning. All people learn better and develop deeper understanding and intuitions if they have the opportunity and the tools to explore their understanding and intuition by going back and forth between different representations of the a given mathematical object and the procedures for manipulating and transforming it. The Cartesian graph provides a way to express functions with imagery in addition to the symbols we usually use for their representation. The increasingly wide availability of graphing calculators and graphing software for personal computers and mobile devices makes it possible for us as teachers to take advantage of graphical representations in the way we teach the mathematics we teach as well as in the way we ourselves understand the subject. Exploring Linear & Quadratic Functions - in one and two variables  Linear functions & yellow bowties   Linear functions & quadrilaterals   Parabolas between parabolas Absolute value functions & quadrilaterals Museum of Mathematics Exhibit   Museum of Mathematics Exhibit II Two Cones and A Plane The locus of the vertex !   Power drill - factoring & FOIL   2D Algebra tiles   Exploring quadratic functions  Joe T's theorem I  Joe T's Theorem II   Linear & Quadratic Functions of two variables Build & Fit applets - the applets in this group allow you to build different sorts of functions graphically and then fit them with appropriate symbolic expressions [or vice versa]   Build & Fit - linear functions   Build & Fit - quadratic functions   The Polynomial Constructor   Build a quadratic from a rectangle   Build & Fit Absolute Value f'n I    Build & Fit Absolute Value f'n II    Build & Fit Absolute Value f'n III      Build & Fit - ellipse    Build & Fit - parabola   Build & Fit - hyperbola Exploring Families of Functions through Transformations -   Function family builder   Constructing f'ns by sliding/stretching/squeezing/reflecting   Turning sine into cosine       Beyond Linear and Quadratic Functions   Power functions - x^n when n is not an integer   Powers functions  - when x is complex   Petals - a polar exploration   Spirals   A Swirl of Spirals Circular & Hyperbolic Trig F'ns   3D Algebra blocks   morphing polynomials  morphing absolute value functions   Approximating functions with polynomials   Exponential Functions   Exponential & Quadratic have a Race - a fable about rate of change   Calculus derivative explorer  integral explorer    Calculus workbench   Some curiosities  'Squaring' the circle  Was Pythagoras wrong?     'Elliptical' Trigonometric Functions     A Line and an Hyperbola   A Bestiary of Curves of degree > 2   f(x) f'(x) puzzle   f(x)/f'(x) puzzle   Was Pythagoras Wrong? - Related Heresies   Pi = 4?   'Polygonal' Trigonometric Functions         f(x)+f'(x) puzzle     What do you now know more about? What surprised you? What would you like to know more about? Judah L. Schwartz mathMINDhabits by Judah L. Schwartz is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.