How to Tell your Asymptote from a Hole in the Graph.

The fifth in the Graphing Calculator / Technology series (The MPAC discussion will continue next week) Seeing discontinuities on a graphing calculator is possible; but you need to know how a calculator graphs to do it. Here’s the story: The number you choose for XMIN becomes the x-coordinate of the (center of) the pixels in the…

Continuity

The definition of continuity of a function used in most first-year calculus textbooks reads something like this: A function f is continuous at x = a if, and only if, (1) f(a) exists (the value is a finite number), (2)  exists (the limit is a finite number), and (3)  (the limit equals the value). A…

Continuity

Limits logically come before continuity since the definition of continuity requires using limits. But practically and historically, continuity comes first. The concept of a limit is used to explain the various kinds of discontinuities and asymptotes. Start by studying discontinuities. Types of discontinuities to consider: removable (a gap or hole in the graph), jump, infinite…