1. Functions,Limits,and Continuity..................................................................................................
Equationsand Graphs
LearningObjectives
A studentwill be able to:
- Find solutionsof graphsof equations.
- Find key propertiesof graphsof equationsincludinginterceptsand symmetry.
- Find pointsof intersectionsof two equations.
- Interpretgraphsas models.
Introduction
In this lessonwe will reviewwhatyou havelearnedin previousclassesaboutmathematicalequationsof
relationshipsand correspondinggraphicalrepresentationsand how theseenableus to addressa rangeof
mathematicalapplications.We will reviewkey propertiesof mathematicalrelationshipsthat will allowus to
solvea varietyof problems.We will examineexamplesof how equationsand graphscan be usedto model
real-lifesituations.
Let’s beginour discussionwith someexamplesof algebraicequations:
Example1: The equationhas orderedpairsof numbers as solutions.Recallthat a particular
pair of numbersis a solutionif directsubstitutionof the and valuesinto the originalequationyieldsa
true equationstatement.In this example,severalsolutionscan be seenin the followingtable:
We can graphicallyrepresentthe relationshipsin a rectangularcoordinatesystem,takingthe as the
horizontalaxis and the as the verticalaxis. Oncewe plot the individualsolutions,we can drawthe curve
throughthe pointsto get a sketchof the graphof the relationship: