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For each listed function, students determine points of discontinuity and holes, find x- and y-intercepts, identify horizontal asymptotes, state the domain restrictions, and describe limit behavior near each vertical asymptote. The problems also require determining end behavior asymptotes and then sketching the resulting graphs accurately.",{"@graph":69,"@context":115},[70,84,106],{"@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/infinite-precalculus-graphs-of-rational-functions-worksheets-02-graphs-of-rational-functions/523484/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/infinite-precalculus-graphs-of-rational-functions-worksheets-02-graphs-of-rational-functions/523484.png","ImageObject",300,407,{"name":92,"@type":93},"PakDamar76","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109],{"name":110,"@type":111,"acceptedAnswer":112},"What is the final step after determining limits and asymptotes?","Question",{"text":113,"@type":114},"Sketch the graph using the identified features so the plotted behavior matches the asymptotes and intercepts.","Answer","https://schema.org",{"og:url":83,"og:type":117,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":119,"canonical":83},"index,follow",{"doc_id":121,"site_id":62},523484,1791710643,{"code":4,"msg":5,"data":124},{"doc_id":121,"user_id":125,"nickname":92,"user_avatar":126,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":127,"file_id":128,"file_url":129,"file_type":130,"file_size":131,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":132,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":133,"faqs":134,"seo_title":135,"seo_description":67,"update_tm":136,"read_time":52,"preview_page_count":4},962090893057,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Precalculus Graphs of Rational Functions  \nName  Date  Period   \nFor each function, identify the points of discontinuity, holes, intercepts, horizontal asymptote, domain, limit behavior at all vertical asymptotes, and end behavior asymptote. Then sketch the graph.  \n1) f (x) 􀀠 x~~ ~~~~ ~~􀀖 􀀎 􀀖  \n2) f (x) 􀀠 􀀐 ~~ ~~x~~ ~~~~ ~~􀀕 􀀐 􀀕  \n3) f (x) 􀀠 xx􀀕~~􀀕 ~~􀀐~~ ~~􀀗􀀜  \n4) f (x) 􀀠 􀀕~~􀀕 ~~􀀐􀀐~~ ~~~~ ~~􀀎~~ ~~􀀔􀀔􀀕~~ ~~􀀙~~ ~~  \n\n| | |  |  |  |  |  |  | y |  |  |  |  |  |  | |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  | 􀀛 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀙 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀗 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀕 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| 􀀐􀀛 | 􀀐 | 􀀙 | 􀀐 | 􀀗 | 􀀐 | 􀀕 |  |  | 􀀕 |  | 􀀗 |  |  | 􀀙 | 􀀛 | x |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀐􀀕 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀐􀀗 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀐􀀙 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  | 􀀐􀀛 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n5) f (x) 􀀠 x 􀀕 􀀎 􀀕x 􀀐 􀀖 􀀐􀀖 x 􀀐 􀀙  \n\n| | |  |  |  |  |  |  | y |  |  |  |  |  |  | |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  | 􀀛 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀙 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀗 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀕 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| 􀀐􀀛 | 􀀐 | 􀀙 | 􀀐 | 􀀗 | 􀀐 | 􀀕 |  |  | 􀀕 |  | 􀀗 |  |  | 􀀙 | 􀀛 | x |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀐􀀕 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀐􀀗 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀐􀀙 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  | 􀀐􀀛 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n6) f (x) 􀀠 􀀕~~ ~~􀀐􀀐􀀐􀀐􀀙􀀛~~ ~~  \n\n| | 􀀛 |  |  |  |  |  |  | y |  |  |  |  |  |  | |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀙 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀗 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀕 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| 􀀐􀀛 | 􀀐 | 􀀙 | 􀀐 | 􀀗 | 􀀐 | 􀀕 |  |  | 􀀕 |  | 􀀗 |  |  | 􀀙 | 􀀛 | x |\n|  |  |  |  |  |  |  | 􀀕 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀐 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀗 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀐 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀙 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀐 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 􀀛 |  |  |  |  |  |  |  |  |  |\n|  | 􀀐\u003Cbr>|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\nKuta Software-Infinite Precalculus Graphs of Rational Functions  \nName  Date  Period   \nFor each function, identify the points of discontinuity, holes, intercepts, horizontal asymptote, domain, limit behavior at all vertical asymptotes, and","cbCaijMx0mylyFYD","https://ap.wps.com/l/cbCaijMx0mylyFYD","pdf",58812,"English","# Functions Analysis\n## Discontinuities and Holes\n## Intercepts and Asymptotes\n## Domain, Limits, and End Behavior\n## Graph Sketching","[{\"question\":\"What is the final step after determining limits and asymptotes?\",\"answer\":\"Sketch the graph using the identified features so the plotted behavior matches the asymptotes and intercepts.\"}]","Infinite Precalculus Graphs of Rational Functions - Worksheets - 02 - Graphs of Rational Functions | PDF",1791426908]