[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522811-105":59,"doc-detail-522811-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","continuity-find-the-intervals-on-which-each-function-is-continuous","Continuity - Find the intervals on which each function is continuous","","Worksheet for Infinite Calculus focused on determining continuity of piecewise and multi-form functions. Tasks require finding the intervals where each given function remains continuous, with optional use of provided graphs to sketch behavior around breakpoints. The problems include multiple numbered functions, including piecewise definitions and composite expressions, followed by additional critical thinking items that ask students to assess whether functions are continuous everywhere, identify discontinuity locations, and classify discontinuity types.",{"@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/continuity-find-the-intervals-on-which-each-function-is-continuous/522811/",{"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/continuity-find-the-intervals-on-which-each-function-is-continuous/522811.png","ImageObject",300,407,{"name":92,"@type":93},"Alex Sinclair","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What are the main instructions for the worksheet?","Question",{"text":113,"@type":114},"Find the intervals on which each function is continuous, and use the provided graphs to sketch the functions when needed.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Do the problems include piecewise functions?",{"text":118,"@type":114},"Yes. Several questions define f(x) in different forms depending on x, requiring interval-based continuity checking.",{"name":120,"@type":111,"acceptedAnswer":121},"What should be done when a function is not continuous?",{"text":122,"@type":114},"Locate the x-axis location(s) of the discontinuity and classify each discontinuity type.","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},522811,1791482563,{"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},1099523882182,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Kuta Software-Infinite Calculus Name   \nContinuity Date  Period   \nFind the intervals on which each function is continuous.  \nx 2 + 2x + 1, x \u003C 1  \n1) f (x) = {− ~~ ~~x~~ ~~ , x ≥ 1  \n2  \n2) f (x) = {13,, xx  55  \n\n| |  |  |  f |  |  |  |  |  |  |  |  |  |  |  | |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  | 10 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | 8 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | 6 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | 4 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | 2 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| − | 2 |  |  | 2 |  | 4 |  | 6 |  |  | 8 | 1 | 0 | 1 | 2 | x |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | −2 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | −4 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  | −6 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\nFind the intervals on which each function is continuous. You may use the provided graph to sketch the function.  \n3) f (x) = {20x, − 10, xx  22  \n\n| | |  |  |  |  | f |  |  |  |  |  |  |  |  | |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  | 4 |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  | 2 |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| −6 | − | 4 | − | 2 |  |  | 2 |  | 4 |  | 6 |  |  | 8 | 1 | 0 x |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  | −2 |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  | −4 |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  | −6 |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  | −8 |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  | − | 10 |  |  |  |  |  |  |  |  |  |  |  |\n|  | |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n4) f ( x) = ~~ ~~x2~~ ~~~~ ~~−1~~ ~~2~~ ~~  \n\n| | |  |  |  |  |  |  |  | f |  |  |  |  |  | |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 4 |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 2 |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| − | 8 | − | 6 | − | 4 | − | 2 |  |  | 2 |  | 4 |  | 6 |  | x |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −2 |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −4 |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −6 |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −8 |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | − | 10 |  |  |  |  |  |  |  |  |\n|  | |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\nFind the intervals on which each function is continuous.  \n5) f ( x) = ~~ ~~2xx~~ ~~4~~ ~~ 6) f (x) = {−x2x2 722x, − 2, xx  00  \n7) f (x) = − ~~ ~~x~~ ~~2~~ ~~−x~~ ~~−3~~ ~~12~~ ~~ 8) f (x) = ~~ ~~x2~~ ~~~~ ~~6~~ ~~  \nDetermine if each function is continuous. If the function is not continuous, find the x-axis location of and classify each disco","cbCaigGAcjkKo5H6","https://ap.wps.com/l/cbCaigGAcjkKo5H6","pdf",46373,"English","# Find intervals of continuity\n## Piecewise functions and graphs\n# Determine continuity and classify discontinuities\n## Critical thinking questions","[{\"question\":\"What are the main instructions for the worksheet?\",\"answer\":\"Find the intervals on which each function is continuous, and use the provided graphs to sketch the functions when needed.\"},{\"question\":\"Do the problems include piecewise functions?\",\"answer\":\"Yes. Several questions define f(x) in different forms depending on x, requiring interval-based continuity checking.\"},{\"question\":\"What should be done when a function is not continuous?\",\"answer\":\"Locate the x-axis location(s) of the discontinuity and classify each discontinuity type.\"}]","Continuity - Find the intervals on which each function is continuous | PDF",1791426195]