[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-523482-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-523482-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","kuta-software-infinite-precalculus-graphs-of-polynomial-functions-worksheets-02","Kuta Software - Infinite Precalculus - Graphs of Polynomial Functions - Worksheets - 02","","Worksheets for Infinite Precalculus focused on graphing polynomial functions. For each given function, tasks require finding real zeros and their multiplicities, identifying x-intercepts that cross the x-axis versus those that do not, and sketching the resulting graph. Additional questions ask students to describe end behavior using limits as x approaches positive and negative infinity, then apply critical-thinking prompts to construct polynomial functions satisfying specified zeros, values, and degree constraints.",{"@graph":14,"@context":73},[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-graphs-of-polynomial-functions-worksheets-02/523482/",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-graphs-of-polynomial-functions-worksheets-02/523482.png","ImageObject",300,407,{"name":42,"@type":43},"jayni","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",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What must be determined for each polynomial function before graph sketching?","Question",{"text":63,"@type":64},"Determine the real zeros and the multiplicity of any repeated zeros, then list x-intercepts where the graph crosses the x-axis and where it does not cross it.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are x-intercepts categorized in these worksheets?",{"text":68,"@type":64},"x-intercepts are split into those where the graph crosses the x-axis and those where it does not cross the x-axis.",{"name":70,"@type":61,"acceptedAnswer":71},"What does the worksheet require for end behavior?",{"text":72,"@type":64},"Students describe end behavior using limits of f(x) as x approaches positive and negative infinity for each function.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},523482,1791732183,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":123,"preview_page_count":4},3985747859343,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Precalculus Graphs of Polynomial Functions  \nName  Date  Period   \nFor each function: (1) determine the real zeros and state the multiplicity of any repeated zeros,(2) list the x-intercepts where the graph crosses the x-axis and those where it does not cross the x-axis, and (3) sketch the graph.  \n1) f (x) 􀀠 􀀐x 􀀖 2) f (x) 􀀠 􀀕x 􀀖 􀀐 􀀖 x 􀀕  \n3) f (x) 􀀠 x 􀀗 􀀎 x 􀀖 􀀐 􀀗x 􀀕 􀀐 􀀗x  \n4) f (x) 􀀠 x 􀀗 􀀎 x 􀀖  \n5) f (x) 􀀠 􀀐x 􀀖 􀀎 􀀙x 􀀕 􀀐 􀀔􀀕x 􀀎 􀀛  \n6) f (x) 􀀠 x 􀀖 􀀐 􀀕x 􀀕  \nDescribe the end behavior of each function.  \n7) f (x) 􀀠 􀀐x 􀀘 􀀎 􀀕x 􀀖 􀀐 x 􀀎 􀀔 8) f (x) 􀀠 􀀕x 􀀕 􀀐 􀀗x 􀀐 􀀖  \n9) f (x) 􀀠 x 􀀗 􀀐 􀀕x 􀀕 􀀐 x 􀀎 􀀔 10) f (x) 􀀠 􀀐x 􀀖 􀀐 􀀜x 􀀕 􀀐 􀀕􀀗x 􀀐 􀀕􀀓  \n11) f (x) 􀀠 􀀐x 􀀘 􀀎 􀀖 x 􀀖 􀀎 􀀔 12) f (x) 􀀠 x 􀀕 􀀎 􀀙x 􀀎 􀀙  \nCritical thinking questions:  \n13) Write a polynomial function f with the 14) Write a polynomial function g with degree  \nfollowing properties: greater than one that passes through the  \n(a) Zeros at 􀀔 , 􀀕 , and 􀀖 points (􀀓 􀀔) (􀀔 􀀔), and (􀀕 􀀔) .(b) f (x) 􀁤 􀀓 for all values of x , , , ,(c) Degree greater than 1  \nKuta Software-Infinite Precalculus Graphs of Polynomial Functions  \nName  Date  Period   \nFor each function: (1) determine the real zeros and state the multiplicity of any repeated zeros,(2) list the x-intercepts where the graph crosses the x-axis and those where it does not cross the x-axis, and (3) sketch the graph.  \n1) f (x) 􀀠 􀀐x 􀀖  \n2) f (x) 􀀠 􀀕x 􀀖 􀀐 􀀖 x 􀀕  \nReal zeros: 􀁞􀀓 mult. 3􀁠  \nx-int, crosses: 􀀓  \nx-int, doesn't cross: None  \nReal zeros: 􀁞 􀀓 mult. 2, ~~ ~~􀀖􀀕  \n􀁠  \nx-int, crosses: 􀀖􀀕  \nx-int, doesn't  \ncross: 􀀓  \n3) f (x) 􀀠 x 􀀗 􀀎 x 􀀖 􀀐 􀀗x 􀀕 􀀐 􀀗x  \n4) f (x) 􀀠 x 􀀗 􀀎 x 􀀖  \nReal zeros: 􀁞􀀓 , 􀀕 , 􀀐􀀕 , 􀀐􀀔􀁠  \nx-int, crosses: 􀀓 , 􀀕 , 􀀐􀀕 , 􀀐􀀔 x-int, doesn't cross: None  \nReal zeros: 􀁞􀀓 mult. 3, 􀀐􀀔􀁠  \nx-int, crosses: 􀀓 , 􀀐􀀔  \nx-int, doesn't cross: None  \n5) f (x) 􀀠 􀀐x 􀀖 􀀎 􀀙x 􀀕 􀀐 􀀔􀀕x 􀀎 􀀛  \nReal zeros: 􀁞􀀕 mult. 3􀁠  \nx-int, crosses: 􀀕  \nx-int, doesn't cross: None  \n6) f (x) 􀀠 x 􀀖 􀀐 􀀕x 􀀕  \nReal zeros: 􀁞􀀓 mult. 2, 􀀕􀁠  \nx-int, crosses: 􀀕 x-int, doesn't cross: 􀀓  \nDescribe the end behavior of each function.  \n7) f (x) 􀀠 􀀐x 􀀘 􀀎 􀀕x 􀀖 􀀐 x 􀀎 􀀔 8) f (x) 􀀠 􀀕x 􀀕 􀀐 􀀗x 􀀐 􀀖  \nlim f (x) 􀀠 􀁦 lim f (x) 􀀠 􀁦 xlf (x) 􀀠 􀀐􀁦 xlf (x) 􀀠 􀁦  \nx􀁯 􀁦 x􀁯 􀁦  \n9) f (x) 􀀠 x 􀀗 􀀐 􀀕x 􀀕 􀀐 x 􀀎 􀀔 10) f (x) 􀀠 􀀐x 􀀖 􀀐 􀀜x 􀀕 􀀐 􀀕􀀗x 􀀐 􀀕􀀓  \nlim f (x) 􀀠 􀁦 lim f (x) 􀀠 􀁦 xlf (x) 􀀠 􀁦 xlf (x) 􀀠 􀀐􀁦  \nx􀁯 􀁦 x􀁯 􀁦  \n11) f (x) 􀀠 􀀐x 􀀘 􀀎 􀀖 x 􀀖 􀀎 􀀔 12) f (x) 􀀠 x 􀀕 􀀎 􀀙x 􀀎 􀀙  \nlim f (x) 􀀠 􀁦 lim f (x) 􀀠 􀁦 xlf (x) 􀀠 􀀐􀁦 xlf (x) 􀀠 􀁦  \nx􀁯 􀁦 x􀁯 􀁦  \nCritical thinking questions:  \n13) Write a polynomial function f with the following properties:  \n(a) Zeros at 􀀔 , 􀀕 , and 􀀖(b) f (x) 􀁤 􀀓 for all values of x (c) Degree greater than 1  \nf (x) 􀀠 􀀐(x 􀀐 􀀔)􀀕 􀂘 (x 􀀐 􀀕)􀀕 􀂘 (x 􀀐 􀀖)􀀕  \n14) Write a polynomial function g with degree greater than one that passes through the points (􀀓 , 􀀔), (􀀔 , 􀀔), and (􀀕 , 􀀔) .  \ng(x) 􀀠 x(x 􀀐 􀀔)(x 􀀐 􀀕) 􀀎 􀀔  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCainJCKHtwwAzT","https://ap.wps.com/l/cbCainJCKHtwwAzT","pdf",45888,"English","# For each function\n## Real zeros and multiplicity\n## x-intercepts: crosses vs. doesn't cross\n## Sketch the graph\n# Describe end behavior\n# Critical thinking questions\n## Construct a polynomial from zeros and conditions\n## Construct a polynomial passing through given points","[{\"question\":\"What must be determined for each polynomial function before graph sketching?\",\"answer\":\"Determine the real zeros and the multiplicity of any repeated zeros, then list x-intercepts where the graph crosses the x-axis and where it does not cross it.\"},{\"question\":\"How are x-intercepts categorized in these worksheets?\",\"answer\":\"x-intercepts are split into those where the graph crosses the x-axis and those where it does not cross the x-axis.\"},{\"question\":\"What does the worksheet require for end behavior?\",\"answer\":\"Students describe end behavior using limits of f(x) as x approaches positive and negative infinity for each function.\"}]","Kuta Software - Infinite Precalculus - Graphs of Polynomial Functions - Worksheets - 02 | PDF",1791426905]