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

Discusses a method of graphing polar equations using information from the Cartesian graphs of trigonometric functions. (MKR)

Investigates the relationship between a fourth-degree polynomial function's parameters and its graph. (MKR)

Presents an activity which focuses on the graph of sine and cosine functions and other properties that can easily be inferred from the graph. (ASK)

Explores an unexpected connection between a function, its inverse, and the arithmetic mean, algebraically and graphically. (MM)

Introduces the concept of function using graphs or pictorial representations of functions. Presents four activities for grade levels 8-14 that use the natural progression from qualitative graphs to quantitative graphs to tables to equations for introducing the theme of distance from an object as a function of time. (Author/NB)

Reports on a study of students' responses to two types of questions on final examinations in calculus. Concludes that the two kinds of understanding--pointwise and across time--are clearly distinguishable. Discusses the differences between these two types of understanding. (ASK)

Presents responses to a problem that appeared in the May 2000 issue. The problem was to determine different ways to divide 8 cookies between 3 people. Includes student work from grades 1, 3, and 5. (KHR)

Uses parametric equations and a graphing calculator to investigate the connections among the algebraic, numerical, and graphical representations of functions. (MKR)

In a classroom environment in which continual access to graphing calculators is assumed, items that have been used to assess students' understanding of functions often are no longer appropriate. Describes strategies for modifying such items including requiring students to explain their reasoning, using calculator-active items, analyzing graphs and…

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)

Three activities with Knuth functions are discussed and illustrated, with sample computer programs listed. (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)

Explores developing a concept image of functions. Includes assessment items, describes students' responses to these items, and interprets those responses. (KHR)