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Results support structured practice of continuity concepts.",{"@graph":14,"@context":65},[15,34,56],{"@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/kuta-software-infinite-precalculus-continuity-worksheet-continuity-and-discontinuity/523466/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/kuta-software-infinite-precalculus-continuity-worksheet-continuity-and-discontinuity/523466.png","ImageObject",300,407,{"name":42,"@type":43},"WPS_1790064749","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59],{"name":60,"@type":61,"acceptedAnswer":62},"What do the “intervals on which the function is continuous” problems ask you to find?","Question",{"text":63,"@type":64},"They require identifying ranges of x where the function remains continuous, typically splitting the real line at the x-values where discontinuities occur.","Answer","https://schema.org",{"og:url":32,"og:type":67,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":69,"canonical":32},"index,follow",{"doc_id":71,"site_id":7},523466,1791481979,{"code":4,"msg":74,"data":75},"success",{"doc_id":71,"user_id":76,"nickname":42,"user_avatar":77,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":78,"file_id":79,"file_url":80,"file_type":81,"file_size":82,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":83,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":84,"faqs":85,"seo_title":86,"seo_description":12,"update_tm":87,"read_time":88,"preview_page_count":4},3985747859154,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Precalculus Continuity  \nName  Date  Period   \nDetermine if each function is continuous at the given x-values. If not continuous, classify each discontinuity.  \n2) f (x) = {, 􀀘 ,  \nx 􀁤 􀀖  \n; at x = 􀀖 x 􀀡 􀀖  \n3) f (x) 􀀠 x~~ ~~􀀕~~ ~~x􀀎~~ ~~x􀀔􀀎~~ ~~􀀕~~ ~~ ; at x = 􀀐􀀖 4) f (x) 􀀠 ~~ ~~􀀕􀀗~~ ~~ ; at x = 􀀐􀀕 and x = 􀀕  \n5) f (x) 􀀠 x~~ ~~~~ ~~􀀔~~ ~~; at x = 􀀐􀀔 6) f (x) = {􀀐x􀀕,􀀎 􀀛 x 􀀐 􀀔􀀙 , xx 􀀟􀁴 􀀖􀀖 ; at x = 􀀖  \nDetermine if each function is continuous. If the function is not continuous, find the x-axis location of and classify each discontinuity.  \n7) f (x) 􀀠 􀀐 ~~ ~~􀀕x~~ ~~􀀕~~ ~~􀀎~~ ~~x~~ ~~􀀎~~ ~~􀀔~~ ~~ 8) f (x) 􀀠 x~~ 􀀕 ~~􀀎~~ ~~x~~ ~~􀀎~~ ~~􀀜~~ ~~  \n9) f (x) 􀀠 x~~ ~~􀀕~~ ~~􀀎x~~ ~~x􀀖􀀎~~ ~~􀀖~~ ~~ 10) f (x) 􀀠 x~~ 􀀕 ~~~~ ~~􀀗x  \n11) f (x) = {􀀗􀀐, 􀀔􀀔 , xx 􀁤􀀡 􀀐􀀕􀀕 12) f (x) 􀀠 xx~~􀀕 ~~􀀎􀀎~~ ~~􀀚􀀖x  \nFind the intervals on which each function is continuous.  \n13) f (x) = {,, xx  􀀗􀀗 14) f (x) = {􀀐􀀕􀀕x, 􀀎 􀀙 , xx 􀀟􀁴 􀀖􀀖 15) f (x) 􀀠 x~~ 􀀕 ~~~~ ~~x􀀔~~ ~~􀀎~~ ~~􀀖~~ ~~ 16) f (x) 􀀠 x􀀕􀀕~~ ~~ 􀀎 􀀗x 􀀎 􀀔􀀓  \n17) f (x) 􀀠 􀀐x 􀀕 􀀐 􀀗x 􀀎 􀀕 18) f (x) 􀀠 􀀐 ~~ ~~x~~ 􀀕 ~~~~ ~~x􀀕􀀎~~ ~~􀀕  \n19) f (x) 􀀠 􀀐 ~~ ~~~~ ~~􀀐􀀐~~ ~~~~ ~~ 20) f (x) 􀀠 x~~ 􀀕 ~~􀀐~~ ~~x~~ ~~􀀎~~ ~~􀀜  \nCritical thinking questions:  \n21) Write a function that has an infinite 22) Write a function that is continuous over discontinuity at x 􀀠 􀀔􀀓􀀓 . (􀀐􀁦 , 􀀓),(􀀓 , 􀀔), and (􀀔 , 􀁦) and  \ndiscontinuous everywhere else.  \nKuta Software-Infinite Precalculus Continuity  \nName  Date  Period   \nDetermine if each function is continuous at the given x-values. If not continuous, classify each  \ndiscontinuity.  \n1) f (x) 􀀠 x~~ 􀀕 ~~x􀀎~~ ~~􀀖~~ ~~x~~ ~~ ; at x = 􀀐􀀖 and x = 􀀓  \nRemovable discontinuity at x = 􀀓 Infinite discontinuity at x = 􀀐􀀖  \n3) f (x) 􀀠 x~~ ~~􀀕~~ ~~x􀀎~~ ~~x􀀔􀀎~~ ~~􀀕~~ ~~ ; at x = 􀀐􀀖  \nContinuous at x = 􀀐􀀖  \n5) f (x) 􀀠 x~~ ~~~~ ~~􀀔~~ ~~; at x = 􀀐􀀔  \nInfinite discontinuity at x = 􀀐􀀔  \n2) f (x) = {, 􀀘 ,  \nx 􀁤 􀀖  \n; at x = 􀀖 x 􀀡 􀀖  \nContinuous at x = 􀀖  \n4) f (x) 􀀠 ~~ ~~􀀕􀀗~~ ~~ ; at x = 􀀐􀀕 and x = 􀀕  \nRemovable discontinuity at x = 􀀐􀀕 Infinite discontinuity at x = 􀀕  \n6) f (x) = {􀀐x􀀕,􀀎 􀀛 x 􀀐 􀀔􀀙 , xx 􀀟􀁴 􀀖􀀖 ; at x = 􀀖  \nJump discontinuity at x = 􀀖  \nDetermine if each function is continuous. If the function is not continuous, find the x-axis location of and classify each discontinuity.  \n7) f (x) 􀀠 􀀐 ~~ ~~􀀕x~~ ~~􀀕~~ ~~􀀎~~ ~~x~~ ~~􀀎~~ ~~􀀔~~ ~~  \nContinuous  \n8) f (x) 􀀠 x~~ 􀀕 ~~􀀎~~ ~~x~~ ~~􀀎~~ ~~􀀜  \nInfinite discontinuity at x = 􀀐􀀖  \n9) f (x) 􀀠 x~~ ~~􀀕~~ ~~􀀎x~~ ~~x􀀖􀀎~~ ~~􀀖~~ ~~ 10)  \nRemovable discontinuity at x = 􀀐􀀖  \n11) f (x) = {􀀗􀀐, 􀀔􀀔 , xx 􀁤􀀡 􀀐􀀕􀀕 12)  \nJump discontinuity at x = 􀀐􀀕  \nFind the intervals on which each function is continuous.  \n13) f (x) = {,, xx  􀀗􀀗(􀀐􀁦 , 􀀗),(􀀗 , 􀁦)  \n15) f (x) 􀀠 x~~ 􀀕 ~~~~ ~~x􀀔~~ ~~􀀎~~ ~~􀀖~~ ~~  \n(􀀐􀁦 , 􀀔),(􀀔 , 􀀖),(􀀖 , 􀁦)  \n17) f (x) 􀀠 􀀐x 􀀕 􀀐 􀀗x 􀀎 􀀕  \n(􀀐􀁦 , 􀁦)  \n19) f (x) 􀀠 􀀐 ~~ ~~~~ ~~􀀐􀀐~~ ~~  \n(􀀐􀁦 , 􀀓),(􀀓 , 􀀔),(􀀔 , 􀁦)  \nCritical thinking questions:  \n21) Write a function that has an infinite discontinuity at x 􀀠 􀀔􀀓􀀓 .  \nf (x) 􀀠 x~~ ~~􀀐~~ ~~􀀔􀀔􀀓􀀓  \n14)  \n16)  \n18)  \n20)  \n22)  \nf (x) 􀀠 x~~ 􀀕 ~~~~ ~~􀀗x  \nRemovable discontinuity at x = 􀀓 Infinite discontinuity at x = 􀀗  \nf (x) 􀀠 xx~~􀀕 ~~􀀎􀀎~~ ~~􀀚􀀖x  \nInfinite discontinuities at x = 􀀐􀀖 , x = 􀀓  \nf (x) = {􀀐􀀕􀀕x, 􀀎 􀀙 , xx 􀀟 􀀖  \n􀁴 􀀖  \n(􀀐􀁦 , 􀀖), [􀀖 , 􀁦)  \nf (x) 􀀠 x􀀕􀀕~~ ~~ 􀀎 􀀗x 􀀎 􀀔􀀓  \n(􀀐􀁦 , 􀁦)  \nf (x) 􀀠 􀀐 ~~ ~~x~~ 􀀕 ~~~~ ~~x􀀕􀀎~~ ~~􀀕~~ ~~  \n(􀀐􀁦 , 􀀔),(􀀔 , 􀀕),(􀀕 , 􀁦)  \nf (x) 􀀠 x~~ 􀀕 ~~􀀐~~ ~~x~~ ~~􀀎~~ ~~􀀜~~ ~~  \n(􀀐􀁦 , 􀀖),(􀀖 , 􀁦)  \nWrite a function that is continuous over (􀀐􀁦 , 􀀓),(􀀓 , 􀀔), and (􀀔 , 􀁦) and discontinuous everywhere else.  \nf (x) 􀀠 ~~ ~~􀀐􀀐~~ ~~  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaivBZU1S1XNeg","https://ap.wps.com/l/cbCaivBZU1S1XNeg","pdf",41405,"English","# Determine Continuity at Given x-Values\n## Classify Discontinuities (Removable, Infinite, Jump)\n# Determine Continuity Intervals\n# Critical Thinking: Construct Functions","[{\"question\":\"What do the “intervals on which the function is continuous” problems ask you to find?\",\"answer\":\"They require identifying ranges of x where the function remains continuous, typically splitting the real line at the x-values where discontinuities occur.\"}]","Kuta Software - Infinite Precalculus Continuity - Worksheet - Continuity and Discontinuity | PDF",1791426889,10,{"code":4,"msg":74,"data":90},[91,95,99,102,107,112,117,122,126,129,132],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":100,"slug":101},70,"exam",{"id":103,"doc_module":4,"doc_module_name":25,"category_name":104,"show_sort_weight":105,"slug":106},5,"Comic",60,"comic",{"id":108,"doc_module":4,"doc_module_name":25,"category_name":109,"show_sort_weight":110,"slug":111},6,"Technology",50,"technology",{"id":113,"doc_module":4,"doc_module_name":25,"category_name":114,"show_sort_weight":115,"slug":116},7,"Healthcare",40,"healthcare",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":119,"show_sort_weight":120,"slug":121},8,"Research & Report",30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":123,"show_sort_weight":124,"slug":125},"Religion & Spirituality",20,"religion-spirituality",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":127,"show_sort_weight":124,"slug":128},"World Cup","world-cup",{"id":88,"doc_module":4,"doc_module_name":25,"category_name":130,"show_sort_weight":88,"slug":131},"Lifestyle","lifestyle",{"id":133,"doc_module":4,"doc_module_name":25,"category_name":134,"show_sort_weight":103,"slug":135},19,"General","general"]