CK12 - Trigonometry

the car’s speedand how efficientlyit can use one gallonof gasoline.The first exampleis differentfrom the
secondbecauseit representsafunction:everyx is pairedwith only one y. Somerelationsare mathematically
important.For example,circlesand ellipsesare graphicalrepresentationsof importantrelationsbetweenx
and y coordinates,but thereis not a uniquey-coordinatefor eachx-coordinate.Becauseof the uniquey for
eachx, functionsplay an importantrole in mathematicsand the science.

We can representfunctionsin manyways.Someof the mostcommonwaysto representfunctionsinclude:
sets of orderedpairs,equations,and graphs.The figurebelowshowsa functiondepictedin eachof these
representations:

Representation Example

Set of orderedpairs (1,3),(2,6),(3,9),(4,12)(a subsetof the orderedpairsfor this function)

Equation y= 3x

Graph

In contrast,the relationshownin the figurebelowisnota function:

Representation Example

Set of orderedpairs (4,2),(4,-2),(9,3),(9,-3)(A subsetof the orderedpairsfor this relation)

Equation x=y^2

Graph

To verifythat this relationis not a function,we mustshowthat at leastonexvalueis pairedwith morethan
oneyvalue.If you look at the first representation,the set of orderedpairs,you can see that 4 is pairedwith