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It also classifies relations as one-to-many, many-to-one, many-to-many, and one-to-one with practice tasks and solutions.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/relations-arrow-diagrams-and-ordered-pairs-14-relations-and-functions/657828/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/relations-arrow-diagrams-and-ordered-pairs-14-relations-and-functions/657828.png","ImageObject",300,407,{"name":42,"@type":43},"miraaa_2004","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How can a relation be represented using an arrow diagram and ordered pairs?","Question",{"text":63,"@type":64},"An arrow diagram lists elements of the input set in one shape and connects them to related elements in the output set using arrows. The same relation can be written as a set of ordered pairs that preserves direction, such as (x,y).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What is the difference between codomain and range?",{"text":68,"@type":64},"The codomain is the entire second set of numbers. The range is the subset of the codomain that is actually connected to some element of the domain by the rule, so it may be smaller than the codomain if some elements are not used.",{"name":70,"@type":61,"acceptedAnswer":71},"What are the main types of relations and how are they identified?",{"text":72,"@type":64},"A relation is one-to-many when one domain element maps to more than one codomain element, and many-to-one when multiple domain elements map to the same codomain element. If both occur, it is many-to-many; if no two domain elements share an image, it is one-to-one. Examples and conclusions are provided to classify given cases.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},657828,1793115903,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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are related tothe other set by a rule.Relations are also described asmappings.When we map a set of numbers ontoanother set of numbers,we often express the rule forthe mapping using mathematical relationships insteadofwords.  \n# Representing relations-Arrow diagrams andOrdered pairs\n\nAn Arrow Diagram is often used to represent arelation.The members of each set are listed inside anenclosed shape and arrows are drawn to connectrelated members.For a relation to exist between thesets,there must be a rule connecting pairs ofelements and this rule must hold for all mappingsfrom set Xto set Y.  \nIn the example,shown below,we define a relationbetween the set {4,5,6,7}and the set {9,10,11,12}as ‘add 5'.Notice that 4 is mapped onto 9,5 onto  \n10,6 onto 11 and 7 onto 12.This is shown bydrawing arrows to connect members of the set X tothe members Y.  \nWe refer to the members of the set Xas the input andmembers of the set Y as the output.The direction ofthe arrows is always from the input to the output.  \nThe mapping can also be represented as the set ofordered pairs:  \n(4,9)(5,10)(6,11)(7,12).  \nThe ordered pair preserves the directional property ofthe relation.It is consistent with the order of points  \nplotted on a Cartesian Plane represented by(x,y).  \n# 14.RELATIONS AND FUNCTIONS\n\nIn the Arrow Diagram that follows,we define arelation between the set{1,2,3,4}and the set {3,6,  \n9,12}as ‘multiply by 3'.Notice that 1 is mappedonto 3,2 onto 6,3 onto 9 and 4 onto 12.The arrowsare drawn from the set X to the set Y.  \nThe mapping can also be represented as the set ofordered pairs:  \n(1,3)(2,6)(3,9)(4,12).  \nIn the mapping below,the members are related to therule.'×2 and then +1'.We may say that x is mappedonto 2x+1.This can be represented as the set ofordered pairs.  \n(7,15)(8,17)(9,19)(10,21)  \nA relation exists between two sets of numbers if wecan find a rule that maps members of the first set(domain)onto members of the second set(codomain).The rule must hold for all possible pairsthat are connected.So that when we select a value ofx,also called an input,and apply the rule of therelation,we obtain the y value,also called the outputWe can also refer to the y value as the image of the xvalue.  \n# Defining a relation\n\nBased on our discussion so far,there are threeconditions that must be present when a relation exist,these are:  \n●  Two sets are involved.  \n·There must be a clear rule describing therelationship.  \n·There is a directional property,that is,therelation is defined from one set called thedomain on to another set called thecodomain.  \n# Codomain and Range\n\nNow assume we define a relation from the set,X={1,2,3,4}to the set,Y={2,3,4,5,6,7,8}.  \nWe will define the relation as x→2x.The arrowdiagram is shown below.Notice that some membersof the set Y are not outputs.These are the oddnumbers 3,5 and 7.  \nThe subset of Y consisting of the even numbers {2,4,  \n6,8}is called the range.  \nThe entire set,Y,is called the codomain.  \nRange is a subset of the codomain  \nThe range is defined as those members of thecodomain that are ‘used’,that is they are connectedto some member of the domain by the rule thatdefines the relation.They are also the output valuesor the images of the input values.  \nIf all the members of the codomain are connected tomembers of the domain,then the range is equal to the  \ncodomain.If this is not so,then the range is a subsetof the codomain.  \nBy defining Y as a set of even numbers {2,4,6,8},we can have the situation where the range is equal tothe codomain.  \nRange is equal to the codomain  \nExample 1  \nA relation is represented by the ordered pairs shownbelow:  \n(1,5)(2,7)(3,9)(4,?)(?,23)  \ni.State the rule for the relation.  \nii.What is the image of4?  \niii.What is the input for an output of 23?  \nSolution  \ni.By inspection,the rule for the relation is 2x+  \n3.  \nii.The image of 4 is calculated by substi","cbCaieJNmHnN9XgS","https://ap.wps.com/l/cbCaieJNmHnN9XgS","pdf",1667843,"English","# RELATIONS\n## Representing relations-Arrow diagrams and Ordered pairs\n## 14.RELATIONS AND FUNCTIONS\n## Defining a relation\n## Codomain and Range\n## Types of Relations","[{\"question\":\"How can a relation be represented using an arrow diagram and ordered pairs?\",\"answer\":\"An arrow diagram lists elements of the input set in one shape and connects them to related elements in the output set using arrows. The same relation can be written as a set of ordered pairs that preserves direction, such as (x,y).\"},{\"question\":\"What is the difference between codomain and range?\",\"answer\":\"The codomain is the entire second set of numbers. The range is the subset of the codomain that is actually connected to some element of the domain by the rule, so it may be smaller than the codomain if some elements are not used.\"},{\"question\":\"What are the main types of relations and how are they identified?\",\"answer\":\"A relation is one-to-many when one domain element maps to more than one codomain element, and many-to-one when multiple domain elements map to the same codomain element. If both occur, it is many-to-many; if no two domain elements share an image, it is one-to-one. Examples and conclusions are provided to classify given cases.\"}]","Relations - Arrow diagrams and Ordered pairs - 14 Relations and Functions | PDF",1792991594,23]