- b.
- c. becauseyou wouldexpect(1) a declineas soonas you boughtthe car, and (2) the valueto be declining
moregraduallyafter the initialdrop. - a. b. The pool has area when
- The rate of changewill be The formulawill be
- At the time or equivalentlyin the year 2112, the car will be valuedat.
- A linearmodelmay not be the best functionto modeldepreciationbecausethe graphof the function
decreasesas time increases;henceat somepointthe valuewill take on negativereal numbervalues,an
impossiblesituationfor the valueof real goodsand products.
Relationsand Functions
LearningObjectives
A studentwill be able to:
- Identifyfunctionsfrom variousrelationships.
- Reviewfunctionnotation.
- Determinedomainsand rangesof particularfunctions.
- Identifykey propertiesof somebasicfunctions.
- Sketchgraphsof basicfunctions.
- Sketchvariationsof basicfunctionsusingtransformations.
- Composefunctions.
Introduction
In our last lessonwe examineda varietyof mathematicalequationsthat expressedmathematicalrelationships.
In this lessonwe will focuson a particularclassof relationshipscalledfunctions,and examinetheir key
properties.We will then reviewhow to sketchgraphsof somebasicfunctionsthat we will revisitlater in this
class.Finally, we will examinea way to combinefunctionsthat will be importantas we developthe key
conceptsof calculus.
Let’s beginour discussionby reviewingfour typesof equationswe examinedin our last lesson.
Example1: