[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522847-105":59,"doc-detail-522847-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","curve-sketching-worksheet","Curve Sketching - Worksheet","","Worksheet for curve sketching in Infinite Calculus, guiding students to analyze each given function systematically. For every problem, students determine the x- and y-intercepts, critical points, and the open intervals of increase/decrease. The tasks also require finding inflection points and classifying concavity as concave up or concave down on corresponding intervals. Finally, students identify relative minima and maxima, then use all results to sketch the graph, with multiple polynomial and rational examples provided.",{"@graph":69,"@context":122},[70,84,105],{"@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/curve-sketching-worksheet/522847/",{"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/curve-sketching-worksheet/522847.png","ImageObject",300,407,{"name":92,"@type":93},"Taylor Morgan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-12","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What information is needed to sketch each function in this worksheet?","Question",{"text":112,"@type":113},"For each function, determine the x- and y-intercepts, critical points, intervals of increasing and decreasing, inflection points, concavity intervals, and relative minima and maxima.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you find where a function is increasing or decreasing?",{"text":117,"@type":113},"Use the critical points to split the real line into open intervals and then determine which intervals the function rises (increasing) or falls (decreasing).",{"name":119,"@type":110,"acceptedAnswer":120},"What determines whether a graph is concave up or concave down?",{"text":121,"@type":113},"Locate the inflection point x-coordinates, then classify each open interval based on whether the function is concave up or concave down on that interval.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522847,1791697150,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":46},1099523885336,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Calculus Name   \nCurve Sketching Date  Period   \nFor each problem, find the: x and y intercepts, x-coordinates of the critical points, open intervals where the function is increasing and decreasing, x-coordinates of the inflection points, open intervals where the function is concave up and concave down, and relative minima and maxima. Using this information, sketch the graph of the function.  \n1) y = − ~~ ~~x33~~ ~~ + x 2  \n\n| | y |\n| --- | --- |\n| −8 −7 −6 −5 −4 −3 −2 −1\u003Cbr>−1\u003Cbr>−2\u003Cbr>−3\u003Cbr>−4\u003Cbr>−5\u003Cbr>−6\u003Cbr>−7\u003Cbr>−8 | 1 2 3 4 5 6 7 8\u003Cbr>x |\n\n2) y = − ~~ ~~x44~~ ~~ + x 2 − 1  \n\n| 8\u003Cbr>7\u003Cbr>6\u003Cbr>5\u003Cbr>4\u003Cbr>3\u003Cbr>2\u003Cbr>1 | y |\n| --- | --- |\n| −8 −7 −6 −5 −4 −3 −2 −1\u003Cbr>−1\u003Cbr>−2\u003Cbr>−3\u003Cbr>−4\u003Cbr>−5\u003Cbr>−6\u003Cbr>−7\u003Cbr>−8 | 1 2 3 4 5 6 7 8\u003Cbr>x |\n\n5 2 3) y = ~~ ~~15(x − 4) 3 + 2(x − 4) 3  \n\n| 8\u003Cbr>7\u003Cbr>6\u003Cbr>5\u003Cbr>4\u003Cbr>3\u003Cbr>2\u003Cbr>1 | y |\n| --- | --- |\n| −8 −7 −6 −5 −4 −3 −2 −1\u003Cbr>−1\u003Cbr>−2\u003Cbr>−3\u003Cbr>−4\u003Cbr>−5\u003Cbr>−6\u003Cbr>−7\u003Cbr>−8 | 1 2 3 4 5 6 7 8\u003Cbr>x |\n\nFor each problem, find the: x and y intercepts, asymptotes, x-coordinates of the critical points, open intervals where the function is increasing and decreasing, x-coordinates of the inflection points, open intervals where the function is concave up and concave down, and relative minima and maxima. Using this information, sketch the graph of the function.  \n4) y =  \n7x 2 − 7  \n3 x  \n\n| | y |\n| --- | --- |\n| −8 −7 −6 −5 −4 −3 −2 −1\u003Cbr>−1\u003Cbr>−2\u003Cbr>−3\u003Cbr>−4\u003Cbr>−5\u003Cbr>−6\u003Cbr>−7\u003Cbr>−8 | 1 2 3 4 5 6 7 8\u003Cbr>x |\n\nKuta Software-Infinite Calculus Name   \nCurve Sketching Date  Period   \nFor each problem, find the: x and y intercepts, x-coordinates of the critical points, open intervals where the function is increasing and decreasing, x-coordinates of the inflection points, open intervals where the function is concave up and concave down, and relative minima and maxima. Using this information, sketch the graph of the function.  \n1) y = − ~~ ~~x33~~ ~~ + x 2  \n\n| \u003Cbr> 8\u003Cbr>7\u003Cbr>6\u003Cbr>5\u003Cbr>4\u003Cbr>3\u003Cbr>2\u003Cbr>1\u003Cbr>| y |\n| --- | --- |\n| −8 −7 −6 −5 −4 −3 −2 −1\u003Cbr>−1\u003Cbr>−2\u003Cbr>−3\u003Cbr>−4\u003Cbr>−5\u003Cbr>−6\u003Cbr>−7\u003Cbr>−8 | 1 2 3 4 5 6 7 8\u003Cbr>x\u003Cbr>|\n\nx-intercepts at x = 0, 3 y-intercept at y = 0  \nCritical points at: x = 0, 2  \nIncreasing: (0, 2)  \nDecreasing: (−∞, 0), (2, ∞)  \nInflection point at: x = 1  \nConcave up: (−∞, 1)  \nConcave down: ( 1, ∞)  \nRelative minimum: (0, 0)  \nRelative maximum: (2, ~~ ~~43)  \n2) y = − ~~ ~~x44~~ ~~ + x 2 − 1  \n\n| | y |\n| --- | --- |\n| −8 −7 −6 −5 −4 −3 −2 −1\u003Cbr>−1\u003Cbr>−2\u003Cbr>−3\u003Cbr>−4\u003Cbr>−5\u003Cbr>−6\u003Cbr>−7\u003Cbr> −8 | 1 2 3 4 5 6 7 8\u003Cbr>x\u003Cbr>|\n\nx-intercepts at x = − 2 , 2  \ny-intercept at y = −1  \nCritical points at: x = − 2 , 0, 2  \nIncreasing: (−∞, − 2 ), (0, 2 )  \nDecreasing: (− 2 , 0), ( 2 , ∞)  \nInflection points at: x = − ~~ ~~3~~ ~~, ~~ ~~3~~ ~~  \nConcave up: (−~~ ~~36 ,~~ ~~36~~ ~~ )  \nConcave down: (−∞, −~~ ~~36~~ ~~ ),(~~ ~~36 , ∞)  \nRelative minimum: (0, −1)  \nRelative maxima: (− 2 , 0), ( 2 , 0)  \n5 2 3) y = ~~ ~~15(x − 4) 3 + 2(x − 4) 3  \n\n| | y | |\n| --- | --- | --- |\n| −8 −7 −6 −5 −4 −3 −2 −1\u003Cbr>−1\u003Cbr> −2\u003Cbr>−3\u003Cbr>−4\u003Cbr>−5\u003Cbr>−6\u003Cbr>−7\u003Cbr>−8 | 1 2 3 4 5 6 7 8\u003Cbr>x |  |\n\nx-intercepts at x = −6, 4  \n3  \ny-intercept at y = ~~ ~~125~~ ~~2 Critical points at: x = 0, 4  \nIncreasing: (−∞, 0), (4, ∞)  \nDecreasing: (0, 4)  \nInflection point at: x = 6  \nConcave up: (6, ∞)  \nConcave down: (−∞, 4), (4, 6)  \nRelative minimum: (4, 0)  \nRelative maximum: (0, ~~ ~~1252 )  \nFor each problem, find the: x and y intercepts, asymptotes, x-coordinates of the critical points, open intervals where the function is increasing and decreasing, x-coordinates of the inflection points, open intervals where the function is concave up and concave down, and relative minima and maxima. Using this information, sketch the graph of the function.  \nx-intercepts at x = −1, 1  \nNo y-intercepts.  \nVertical asymptote at: x = 0  \nHorizontal asymptote at: y = 0  \nCritical points at: x = − 3 , 3  \nIncreasing: (− 3 , 0), (0, 3 )  \nDecreasing: (−∞, − 3 ), ( 3 , ∞)  \nInflection points at: x = − 6 , 6  \nConcave up: (− 6 ,","cbCaiuASNoWtfAAw","https://ap.wps.com/l/cbCaiuASNoWtfAAw","pdf",56005,"English","# Curve Sketching Tasks\n## Intercepts, Critical Points, and Increasing/Decreasing Intervals\n## Inflection Points, Concavity, and Relative Min/Max","[{\"question\":\"What information is needed to sketch each function in this worksheet?\",\"answer\":\"For each function, determine the x- and y-intercepts, critical points, intervals of increasing and decreasing, inflection points, concavity intervals, and relative minima and maxima.\"},{\"question\":\"How do you find where a function is increasing or decreasing?\",\"answer\":\"Use the critical points to split the real line into open intervals and then determine which intervals the function rises (increasing) or falls (decreasing).\"},{\"question\":\"What determines whether a graph is concave up or concave down?\",\"answer\":\"Locate the inflection point x-coordinates, then classify each open interval based on whether the function is concave up or concave down on that interval. \"}]","Curve Sketching - Worksheet | PDF",1791426231]