Describes an approach to the initial teaching of composite functions that relies primarily on mapping representations. (MKR)

Explores the effects of varying the coefficients in the general quadratic function using graphing calculators. (MKR)

Four noncommutative groups are given, to be used by students to construct the operation tables and verify that each structure is noncommutative. (MNS)

Suggests that, for some classes of functions, an algebraic method is available that provides a nonstandard application of the discriminant conditions as well as an exact method of optimization for precalculus students. Examples are given, and students should compare these methods with others regarding generality, ease, and efficiency. (AIM)

Presents a classification of factorable cubics and shows how the associated factor graphs determine domains of disconnected branches and furnish a skeletal framework for the number and shape of the branches. Illustrates three dimensional visualization and examines level curves and spikes of surfaces. (KHR)

Much can be learned from a study of rational functions and the behavior of their graphs, so their inclusion in secondary school mathematics textbooks is urged. Analysis of reciprocal relationships and when they don't apply, asymptotes, and the graphing technique are each included in the discussion. (MNS)

Describes an activity in which students are given a set of designs and are required to use their electronic grapher to reproduce the designs. The activity reinforces students' understanding of lines and of the formula for a linear function. (MKR)

Presents a method for introducing students to broken-line functions with unbroken domains. Concludes that a unit on broken-line functions should enhance students' understanding of the function concept. (ASK)

A drill-and-practice game called "Digits Delight"; the story of Parabella (and Hyp and Elli); and a method for finding inverse functions, using Rubik's cube and algebra, are included. (MNS)

Examples for determining the equation of a line through two points or a quadratic function that contains three noncollinear points are presented. (MNS)

Discusses how students fail to recognize the underlying equivalence when the same set of points is represented by a graph or an equation or a table. Presents activities in which more than one form of representations of the same information are included. (ASK)

Develops a method for visualizing the complex roots of a polynomial equation. Illustrates some quadratic or cubic polynomials and their solutions. (KHR)

Presents an alternate approach to teaching quadratics by fully integrating the study of quadratic equations and quadratic functions using graphs. Includes reproducible student worksheets. (MKR)

Presents a teacher's guide and reproducible student worksheets to develop the procedure for finding the inverse of a function. (MKR)

Presents an investigation of a third-degree polynomial using a TI-82 graphing calculator. Also includes an algebraic solution. (MKR)