Casio ED-WKBK-PRECALC Datasheet download pdf (Page 42)

A Graphical Look At Continuity Teacher Notes

Topic: Continuity

NCTM Standard

• Organize and consolidate their mathematical thinking through

communication; communicate their mathematical thinking coherently and

clearly to peers, teacher, and others.

Objectives

The student will be able to develop a visual understanding of how limits and

continuity relate and be able to understand and communicate what it means

for a function to be continuous at a point.

Getting Started

This activity will have students explore the concept of continuity at a point. It

will also allow them to discover that simply having a limit at a point will not

guarantee that the function is also continuous. It also explores the idea that

having a limit is a necessary, but not a sufficient condition to determine the

continuity of a function at a point, and through all points.

Prior to using this activity:

• Students should be able to produce and manipulate graphs of functions

manually and a graphing calculator.

• Students should be able to produce split-defined (or piecewise) functions.

• Students should have a basic understanding of the language of limits.

Ways students can provide evidence of learning:

• Students should be able to produce graphs of functions and communicate

symbolically, graphically and verbally the relationship between having a

limit and being continuous.

Common mistakes to be on the lookout for:

• Students may produce a graph on the calculator and not be able to

communicate the concept of a split-defined function because the window

chosen may produce the appearance of a single unbroken formula.

• Students may confuse the pixel values with the actual function values.

Definitions:

• Asymptote

• Continuity

• Discontinuity

• Limit

• Parabola

• Vertex

Activity 4 • Calculus with the Casio fx-9750GII

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Casio ED-WKBK-PRECALC Datasheet Page 42