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Students learn to graph functions from an equation by constructing a table of values, plotting points, and applying the vertical line test to decide whether a relation is a function.",{"@graph":14,"@context":66},[15,34,49],{"@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/functions-lesson-mathematics-lesson-for-middle-school/180851/",4,{"url":32,"name":10,"@type":35,"author":36,"headline":10,"publisher":39,"fileFormat":42,"inLanguage":8,"description":12,"dateModified":43,"datePublished":43,"encodingFormat":42,"isAccessibleForFree":44,"interactionStatistic":45},"DigitalDocument",{"name":37,"@type":38},"Riley","Person",{"url":19,"name":40,"@type":41},"DocShare","Organization","application/vnd.openxmlformats-officedocument.presentationml.presentation","2026-09-02",true,{"@type":46,"interactionType":47,"userInteractionCount":4},"InteractionCounter",{"@type":48},"ViewAction",{"@type":50,"mainEntity":51},"FAQPage",[52,58,62],{"name":53,"@type":54,"acceptedAnswer":55},"What is the difference between a relation and a function?","Question",{"text":56,"@type":57},"A relation is any set of ordered pairs representing a relationship. A function is a special relation where each input has exactly one output.","Answer",{"name":59,"@type":54,"acceptedAnswer":60},"How can you tell if a graph represents a function?",{"text":61,"@type":57},"Use the vertical line test: if every vertical line touches the graph only once, the relation is a function.",{"name":63,"@type":54,"acceptedAnswer":64},"How do you graph a function using a table of values?",{"text":65,"@type":57},"Construct the table by substituting x-values into the rule (for example, y = 2x), then plot the coordinate pairs on the graph.","https://schema.org",{"og:url":32,"og:type":68,"og:title":10,"og:site_name":40,"og:description":12},"article",{"robots":70,"canonical":32},"index,follow",{"doc_id":72,"site_id":7},180851,1788342424,{"code":4,"msg":75,"data":76},"success",[77,81,85,88,93,98,103,108,113,116,120],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":78,"show_sort_weight":79,"slug":80},"Story & 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OUTLINE\nWhat are relations?\nWhat are functions?\nPresenting functions as tables and graphs\nThe Vertical Line Test\nx\ny\nDo you still remember how to fill in the table of values based on a given graph?\nComplete the table of values below.\nLET'S RECALL AND ANALYZE!\n12\ny\nx\n10\n8\n6\n4\n2\n2\n4\n6\n8\n10\n12\nLEARNING OUTCOMES\nBy the end of the lesson, you'll be able to:\nExpress relations and functions in tables and graphs.\nDifferentiate between a relation and a function.\nUse a vertical test.\nName\nAlex\nJude\nArlo\nCasey\nAge\n9\n12\n11\n11\nWHAT ARE RELATIONS?\nExample:\nNames and their age are a set of ordered pairs that we could put into a table.\nA relation is a set of ordered pairs that represent a relationship.\nA function is a special type of relation where each input only has one output.\nFunctions are a way of connecting input values to their corresponding output values.\nThe relation is a function if, for every x-value, there is exactly one y-value.\nWHAT IS A FUNCTION?\nFunctions are a way of connecting input values to their corresponding output values.\nExample:\nOrdering a coffee for $5\nPay $5, and you get 1 coffee.\nPay $10, and you'll get 2 coffees, and so on.\nThe input affects the output in a predictable way.\nWHAT IS A FUNCTION?\n1\n-1\n0\n2\n4\n1\n-2\n2\n-1\n3\nx\n-1\n0\n1\n2\ny\n-2\n0\n2\n4\nStep 1:\nStep 2:\ny\nx\nPlot the points.\nConstruct the table of values.\nDo this by substituting values of x to y=2x.\nNotice that for every value of x, there is only one value of y.\nGRAPHING A FUNCTION USING THE TABLE OF VALUES\nGiven the equation y = 2x.\nx\n-6\n-3\n2\n7\n9\n9\n10\ny\n-18\n-16\n-15\n-2\n-4\n11\n-9\nIs this relation a function?\nTRY THIS!\n4\n5\n4\n5\n1\n-2\n-3\n2\n-1\n3\n-4\n-5\n1\n2\n3\n-1\n-2\n-3\n-4\n-5\nUse the vertical line test to check whether a graph of a relation is a function.\nVERTICAL LINE TEST\nIf a vertical line, drawn anywhere on the graph, can touch the graph only once, then it is a function.\n5\n4\n5\n1\n-2\n-3\n2\n-1\n3\n-4\n-5\n1\n2\n3\n4\n-1\n-2\n-3\n-4\n-5\nIf a vertical line, drawn anywhere on the graph, can touch the graph more than once, then the relation is not a function.\nVERTICAL LINE TEST\nA function is a special type of relation where each input only has one output.\nGraphing a function using the table of values\nStep 1: Construct the table of values.\nStep 2: Plot the points on the coordinate plane.\nSUMMARY\nSelect 10 clothing items from your closet. Create a mapping diagram to record the colors to each of the clothing you have.\nThen, find out if the information you collected represents a function or not.\nShare your findings with the class next session.\nCLOSET COLORS!\nREFERENCE\nMathspace. “6.0 Functions and relations | Grade 8 Math | Common Core 8 - 2023 Edition.” Accessed 12 June 2023,\nhttps://mathspace.co/textbooks/syllabuses/Syllabus-1157/topics/Topic-21908/subtopics/Subtopic-279918/?searchString=\nUse these design resources in your Canva Presentation.\nYou can find these fonts online too. Happy designing!\nResource Page\nThis presentation template uses the following free fonts:\nTitles:  Changa\nHeaders:  Changa\nBody Copy: Yantramanav\nCredits\nHappy designing!\nThis presentation template is free for everyone to use thanks to the following:\nSlidesCarnival for the presentation template\nPexels for the photos","cbCaimifwiJeoWhp","https://ap.wps.com/l/cbCaimifwiJeoWhp","pptx",1943482,"English","# Lesson Outline\n## What are relations?\n## What are functions?\n## Presenting functions as tables and graphs\n## The Vertical Line Test\n# Learning Outcomes\n# What Is a Function?\n## Ordering a coffee example\n# Graphing a Function Using the Table of Values\n# Try This!\n# Summary\n# Closet Colors!","[{\"question\":\"What is the difference between a relation and a function?\",\"answer\":\"A relation is any set of ordered pairs representing a relationship. 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