Continuity
LearningObjectives
A studentwill be able to:
- Learnto examinecontinuityof functions.
- Find one-sidedlimits.
- Understandpropertiesof continuousfunctions.
- Solveproblemsusingthe Min-Maxtheorem.
- Solveproblemsusingthe IntermediateValue Theorem.
Introduction
In this lessonwe will discussthe propertyof continuityof functionsand examinesomevery importantimpli-
cations.Let’s start with an exampleof a rationalfunctionand observeits graph.Considerthe following
function:
We knowfrom our studyof domainsthat in orderfor the functionto be defined,we mustuse
Yet whenwe generatethe graphof the function(usingthe standardviewingwindow),we get the following
picturethat appearsto be definedat :
The seemingcontradictionis due to the fact that our originalfunctionhad a commonfactorin the numerator
and denominator, that cancelledout and gaveus a picturethat appearsto be the graphof