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Learners compare a relation with a function by checking whether each input has exactly one output, then apply the vertical line test to decide if a graph represents a function. The lesson includes recalling skills from graph-to-table tasks, working with an example equation y = 2x, and completing a try-this activity using mapping and graph reasoning to verify results.",{"@graph":69,"@context":116},[70,84,99],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/functions-lesson-mathematics-lesson-for-middle-school/180848/",{"url":83,"name":65,"@type":85,"author":86,"headline":65,"publisher":89,"fileFormat":92,"inLanguage":63,"description":67,"dateModified":93,"datePublished":93,"encodingFormat":92,"isAccessibleForFree":94,"interactionStatistic":95},"DigitalDocument",{"name":87,"@type":88},"Riley","Person",{"url":74,"name":90,"@type":91},"DocShare","Organization","application/vnd.openxmlformats-officedocument.presentationml.presentation","2026-09-02",true,{"@type":96,"interactionType":97,"userInteractionCount":4},"InteractionCounter",{"@type":98},"ViewAction",{"@type":100,"mainEntity":101},"FAQPage",[102,108,112],{"name":103,"@type":104,"acceptedAnswer":105},"What is the difference between a relation and a function?","Question",{"text":106,"@type":107},"A relation is a set of ordered pairs showing a relationship. A function is a special relation where each input has exactly one output.","Answer",{"name":109,"@type":104,"acceptedAnswer":110},"How can you tell if a graph is a function?",{"text":111,"@type":107},"Use the vertical line test: if any vertical line touches the graph only once, it is a function.",{"name":113,"@type":104,"acceptedAnswer":114},"How do you graph a function using a table of values?",{"text":115,"@type":107},"First construct the table of values by substituting x into y = 2x, then plot the corresponding points on the coordinate plane.","https://schema.org",{"og:url":83,"og:type":118,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":120,"canonical":83},"index,follow",{"doc_id":122,"site_id":62},180848,1788342404,{"code":4,"msg":5,"data":125},{"doc_id":122,"user_id":126,"nickname":87,"user_avatar":127,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":128,"file_id":129,"file_url":130,"file_type":131,"file_size":132,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":8,"language":133,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":134,"faqs":135,"seo_title":136,"seo_description":67,"update_tm":123,"read_time":81},1374391975076,"https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051","FUNCTIONS LESSON\nMathematics Lesson or Middle School\nLESSON 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","cbCaie1DeLT9qLNt","https://ap.wps.com/l/cbCaie1DeLT9qLNt","pptx",1765726,"English","# Lesson Outline\n## What are Relations?\n## What is a Function?\n## Graphing a Function Using the Table of Values\n## Try This - Vertical Line Test\n## Summary","[{\"question\":\"What is the difference between a relation and a function?\",\"answer\":\"A relation is a set of ordered pairs showing a relationship. A function is a special relation where each input has exactly one output.\"},{\"question\":\"How can you tell if a graph is a function?\",\"answer\":\"Use the vertical line test: if any vertical line touches the graph only once, it is a function.\"},{\"question\":\"How do you graph a function using a table of values?\",\"answer\":\"First construct the table of values by substituting x into y = 2x, then plot the corresponding points on the coordinate plane.\"}]","FUNCTIONS LESSON - Mathematics Lesson for Middle School | PPTX"]