2.1

Algebra 2 Notes2.1 Relations and FunctionsRelation(ship) AdviceIf you have a loved one think about how your relationship worksNormally if you put work into your relationship, you are going to get results out of it. (Hopefully the results you want and you do not break-up)Example: If the female cooks and cleans (input) for the male, hopefully the result (output) will be that the male will buy her jewelry and flowers.Vocabulary Sheet

A Relation in Mathematics

RelationDefinitionA relation is a set of pairs of input and output values.Think about substituting some number in for the variable x in some algebraic equation.Input: number in for xOutput: number you get after solving equationFacts/CharacteristicsMultiple Ways to Represent a Relation:Ordered pairs: {(1,2), (2,4)}Input/Output TablePoints on Coordinate planeMapping diagramEquationSentence/WordsExamples of Relations{(4,7), (3,2), (0,0), (-1, -4)}

XY 01-2437Non-Examples of Relations4 (constant)y (variable)7z (expression)

DomainDomain of a RelationDefinition:The set of all inputs or x-coordinatesFacts/CharacteristicsRange will ALWAYS depend on the domainExamplesRelation: {(0, 3), (2,9), (-3,5)}Domain of this relation: {0, 2, -3}

Relation:-101Domain: {heart, star, smiley face}Non-ExamplesRelation: {(0,1), (2,3), (4,5)}Domain is NOT: {1,3,5}

RangeDefinition of RangeThe set of all outputs or y-coordinatesFacts/CharacteristicsDomain CodomainRange:{A,B}ABCRange is a subset of the codomain!ExamplesRange: {Fred, Peter, James}Beth

Jennifer

BrittanyFredGeorgePeterEricJames{(0,1),(1,1),(4,6),(8,-1)}

Range: {-1,1,6}Relation:Non-ExamplesRange is NOT {Beth, Jennifer, Brittany}Beth

Jennifer

BrittanyFredGeorgePeterEricJamesRelation:{(0,1),(1,1),(4,6),(8,-1)}

Range is NOT: {0,1,4,8}A Special Type of Relation(ship)Think about your loved one againYou SHOULDNT be dating anyone else, so you should only be connected with your significant other thats the only way a RELATION(ship) FUNCTIONS

Bob cannot FUNCTION correctly because he is connected to two girls at the same time.BOBShirleyAprilFUNCTIONSDefinition: a relation where every input has exactly one output

Facts/Characteristics: Vertical Line Test if a vertical line passes through the graph and touches it more than once, then the graph is NOT a functionExamples{(1,2), (2,2), (3,2), (4,2)}

XY102130Non-ExamplesInputsOutputs1

2A

BXY121315110125

Two different types of FunctionsOne-to-One FunctionsOnto FunctionsOne-to-One FunctionsDefinition: Every element of the range of the function corresponds to exactly one element of the domain

Facts/Characteristics:Written 1-1 Horizontal Line Test: determines if a function is 1-1Examples of 1-1 Function1234ABCDENon-Examples of 1-1 Functions1234XYZ

Onto FunctionsDefinition: each element of the range corresponds to an element of the domain

Facts/CharacteristicsAlso called Surjective functionFor all elements b in B there is an element a in A such that f(a)=b.Whole codomain will be the range!Examples of Onto FunctionsABCD123Non-Examples of Onto FunctionsABC1234What we need to knowGraphing a RelationFind domain and range of a relationMake a mapping diagramIdentify if a relation is a functionFunction NotationGraph the Relation{(-2,4), (3,-2), (-1,0), (1,5)}

Find the domain and range of the plotted points.Make a Mapping DiagramFor the relation {(-1,-2), (3, 6), (-5, -10), (3,2)}Identifying FunctionsDetermine whether the relation is a function.A)B)-205-134-1023-135Function Notation