[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522678-105":59,"doc-detail-522678-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","graphing-rational-functions-practice-worksheet","Graphing Rational Functions - Practice Worksheet","","Practice worksheet for Algebra 2 focused on graphing rational functions. Learners identify key features for each given function, including points of discontinuity, holes, vertical asymptotes, x-intercepts, and the horizontal asymptote, then sketch the corresponding graph. Additional prompts require finding discontinuities, holes, vertical asymptotes, and horizontal asymptotes together before graphing. Designed to build skill with analyzing rational expressions and translating properties into accurate graph behavior.",{"@graph":69,"@context":123},[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/graphing-rational-functions-practice-worksheet/522678/",{"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/graphing-rational-functions-practice-worksheet/522678.png","ImageObject",300,407,{"name":92,"@type":93},"Mia  ","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",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What do you need to identify for each rational function?","Question",{"text":113,"@type":114},"You identify points of discontinuity and holes, along with vertical asymptotes and horizontal asymptotes. The worksheet also includes x-intercepts when specified.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What does the worksheet ask you to do after identifying features?",{"text":118,"@type":114},"After determining the features, you sketch the graph that matches the rational function’s behavior near asymptotes and discontinuities.",{"name":120,"@type":111,"acceptedAnswer":121},"How are holes and discontinuities handled in the problems?",{"text":122,"@type":114},"The worksheet separately requires locating holes and points of discontinuity for each function, then using those locations to guide the graph sketch.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},522678,1791494951,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":52,"preview_page_count":4},687207024478,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Algebra 2 Name   \nGraphing Rational Functions Date  Period   \nIdentify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of each.  \n1) f (x) = ~~ ~~􀀖~~ ~~x~~ 􀀕 ~~􀀎~~ ~~􀀔􀀖x~~ ~~􀀐~~ ~~􀀔􀀛~~ ~~ 2) f (x) = xx~~ ~~􀀐~~ ~~􀀕􀀗~~ ~~  \n3) f (x) = 􀀐􀀖x􀀕􀀖~~ ~~ 4) f (x) = 􀀐􀀗􀀕~~ ~~~~ ~~~~ ~~~~ ~~􀀔􀀕~~ ~~  \nIdentify the points of discontinuity, holes, vertical asymptotes, and horizontal asymptote of each. Then sketch the graph.  \n5) f (x) = 􀀐 ~~ ~~x~~ 􀀕 ~~~~ ~~􀀖~~ ~~x~~ ~~  \n7) f (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) = 􀀐~~ ~~􀀐􀀐􀀗􀀔􀀙~~ ~~  \nx 􀀖 􀀐 􀀜x 8) f (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\n􀀖 x 􀀕 􀀐 􀀔􀀕x 9) f (x) = x 􀀕 􀀐 􀀕x 􀀐 􀀖   \n\n|  |  | 􀀛 |  |  |  |  |  |  | y |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 􀀙 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 􀀗 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 􀀕 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| 􀀐 | 􀀛 | 􀀐 | 􀀙 | 􀀐 | 􀀗 | 􀀐 | 􀀕 |  |  | 􀀕 |  | 􀀗 |  | 􀀙 |  | 􀀛 | x |\n|  |  |  |  |  |  |  |  | 􀀕 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 􀀐 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 􀀗 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 􀀐 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 􀀙 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 􀀐 |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |","cbCaih2NheTjGojZ","https://ap.wps.com/l/cbCaih2NheTjGojZ","pdf",57168,"English","# Identify Function Features\n## Discontinuity and Holes\n## Vertical and Horizontal Asymptotes\n## Intercepts and Graph Sketching","[{\"question\":\"What do you need to identify for each rational function?\",\"answer\":\"You identify points of discontinuity and holes, along with vertical asymptotes and horizontal asymptotes. The worksheet also includes x-intercepts when specified.\"},{\"question\":\"What does the worksheet ask you to do after identifying features?\",\"answer\":\"After determining the features, you sketch the graph that matches the rational function’s behavior near asymptotes and discontinuities.\"},{\"question\":\"How are holes and discontinuities handled in the problems?\",\"answer\":\"The worksheet separately requires locating holes and points of discontinuity for each function, then using those locations to guide the graph sketch.\"}]","Graphing Rational Functions - Practice Worksheet | PDF",1791426047]