FunctionComposition
The last topic for this lessoninvolvesa way to combinefunctionscalledfunctioncomposition. Composition
of functionsenablesus to considerthe effectsof one functionfollowedby another. Our last exampleof
graphingby transformationsprovidesa nice illustration.We can think of the final graphas the effect of taking
the followingsteps:
We can thinkof it as the applicationof two functions.First, takes to and then we apply
a secondfunction, to those -values,with the secondfunctionadding to eachoutput.We would
writethe functionsas
where and We call this operationthe
composingof with and use notation Notethat in this example, Verify this fact
by computing right now. (Note:this fact can be verifiedalgebraically, by showingthat the expressions
and differ, or by showingthat the differentfunctiondecompositionsare not equalfor a specific
value.)
LessonSummary
- Learnedto identifyfunctionsfrom variousrelationships.
- Reviewedthe use of functionnotation.
- Determineddomainsand rangesof particularfunctions.
- Identifiedkey propertiesof basicfunctions.
- Sketchedgraphsof basicfunctions.
- Sketchedvariationsof basicfunctionsusingtransformations.