[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-449184-105":59,"doc-detail-449184-en":124},{"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":117,"head_meta":119,"extra_data":121,"updated_unix":123},105,"en","113-function-model-selection-practice","1.13 Function Model Selection - Practice","","Practice on selecting and justifying linear, quadratic, or cubic function models using differences and second/third difference patterns. Includes calculator-based application problems where a given function models painkiller amount, requiring evaluation, restricted domain/range, average rate of change, and maximum value in context. Further piecewise-function tasks model strawberry pricing with a pints limit and patient insulin levels over time, requiring domain/range interpretation and average rate of change meaning. Multiple-choice questions assess the correct model type, zeros, and supporting reasoning.",{"@graph":69,"@context":116},[70,84,99],{"@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/113-function-model-selection-practice/449184/",{"url":83,"name":65,"@type":85,"author":86,"headline":65,"publisher":89,"fileFormat":92,"inLanguage":63,"description":67,"dateModified":93,"datePublished":93,"encodingFormat":92,"isAccessibleForFree":94,"interactionStatistic":95},"DigitalDocument",{"name":87,"@type":88},"Alex Sinclair","Person",{"url":74,"name":90,"@type":91},"DocShare","Organization","application/pdf","2026-09-30",true,{"@type":96,"interactionType":97,"userInteractionCount":4},"InteractionCounter",{"@type":98},"ViewAction",{"@type":100,"mainEntity":101},"FAQPage",[102,108,112],{"name":103,"@type":104,"acceptedAnswer":105},"How do you determine whether data is modeled by a linear, quadratic, or cubic function?","Question",{"text":106,"@type":107},"Use finite differences: constant first differences indicate linear, constant second differences indicate quadratic, and constant third differences indicate cubic. The practice section explicitly links each answer choice to the relevant nonzero constant difference level.","Answer",{"name":109,"@type":104,"acceptedAnswer":110},"In the painkiller problem, how do you interpret f(2) and the average rate of change from t=1 to t=2?",{"text":111,"@type":107},"Evaluate the function at the given time to get the amount in the bloodstream at that hour. Compute the average rate of change between the two times to find how fast the amount is leaving the bloodstream over that interval, explained in context as a per-hour change.",{"name":113,"@type":104,"acceptedAnswer":114},"How are the domain and range handled for the rectangle-in-a-circle and the strawberry/insulin piecewise contexts?",{"text":115,"@type":107},"For the rectangle area function, the restricted domain is based on the rectangle width limits from the circle diameter, and the restricted range covers achievable areas. For strawberries and insulin, domain reflects allowed quantities/time and range reflects feasible prices or insulin levels, with explanations tied to context.","https://schema.org",{"og:url":83,"og:type":118,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":120,"canonical":83},"index,follow",{"doc_id":122,"site_id":62},449184,1790729492,{"code":4,"msg":5,"data":125},{"doc_id":122,"user_id":126,"nickname":87,"user_avatar":127,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":128,"file_id":129,"file_url":130,"file_type":131,"file_size":132,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":133,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":134,"faqs":135,"seo_title":136,"seo_description":67,"update_tm":123,"read_time":39},1099523882182,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","1.13 Function Model Selection  \nAP Precalculus  \n1.13 Practice  \n\n| Select the appropriate model for the data (linear/quadratic/cubic). Explain why it models the data. |  |\n| --- | --- |\n| 1.\u003Cbr>x 1 2 3 4 5 6 y 4 15 50 121 240 419\u003Cbr>\u003Cbr>Cubic, third difference constant of 12. | 2.\u003Cbr>x 1 2 3 4 5 6 y 49 46 43 40 37 34\u003Cbr>\u003Cbr>Linear, first difference constant of െ3 . |\n| 3.\u003Cbr>x 1 2 3 4 5 6 y 119 110 95 74 47 14\u003Cbr>\u003Cbr>Quadratic, second difference constant of െ6 | 4.\u003Cbr>x 2 4 5 6 7 8 y 23 81 122 171 228 293\u003Cbr>\u003Cbr>Quadratic, second difference constant of 32 |\n| CALCULATOR ACTIVE. Use the model to answer the questions in context. |  |\n\n5. A patient receives a dose of painkiller. The function 􀝌ሺ􀝐ሻ ൌ ଶ௧௧మయାାଵଵ଴௧ models the amount of painkiller in the bloodstream over time, where t is time in hours and p is painkiller in milligrams.  \na. Find 􀝌ሺ2ሻ . Explain your solution in context.  \n􀝂ሺ2ሻ ൌ 3.111  \nTwo hours after taking the painkiller, there was 3.111 mg of painkiller in the blood stream.  \nb. What is the average rate of change from 􀝐 ൌ 1 to 􀝐 ൌ 2 ? Explain your solution in context.  \n଺.~~ ~~ଵଶଵଵ ൌ െ 2.889 The painkiller is leaving the blood stream at 2.889 mg per hour.  \nc. What is the maximum amount of painkiller in the patient’s bloodstream?  \n6.161 mg  \n6. A rectangle is inscribed in a circle with diameter of 12 cm. The width of the rectangle is 􀝔 cm. The function  \n􀜣ሺ􀝔ሻ ൌ 􀝔√144 െ􀝔 ଶ models the area of the rectangle.  \na. What is the restricted domain of the function?  \n0 ൏ 􀝔 ൏ 12  \nb. What is the restricted range of the function?  \n0 ൏ 􀝕 ൑ 72  \nc. What is the maximum area of the rectangle?  \n72 cmଶ  \n© The Algebros [from FlippedMath.com](from FlippedMath.com)  \nUse the graph of the piecewise function to answer the questions in context.  \n7. Generic Strawberry Fields allows customers to pay $5 to pick strawberries plus 50 cents for every pintor partial pint of strawberries that they pick. There is a limit of 8 pints per customer. The piecewise function f shown below models the price of strawberries picked.  \na. What is the domain in this context?  \n0 ൑ 􀝔 ൑ 8 pints of strawberries  \nb. The range can be represented by 􀝕 ൌ 5 ൅ 0.5􀝔 where x is integers in the domain. Explain why.  \nThe range starts at 5 and increases in increments of 0.50. Using only integers for the domain generates the range of 5, 5.5, 6,  \n6.5, 7, 7.5, 8, 8.5, 9  \nc. Find 􀝂ሺ3.5ሻ . What does it mean in this context?  \n􀝂ሺ3.5ሻ ൌ 7 3.5 pints of strawberries cost 7 dollars.  \n8. The piecewise function f shown below models the insulin levels of a patient over time where 􀝔 ൌ 0 represents 8:00 .  \na. What is the domain in this context?  \n0 ൑ 􀝔 ൑ 10 hours after 8:00  \nb. What is the range in this context?  \nThis patients insulin levels are 8 ൑ 􀝕 ൑ 24  \nPossible insulin levels are 0 ൑ 􀝕 ൑ 􀜽􀝎􀝋􀝑􀝊􀝀 35 for most patients.  \nc. Find 􀝂ሺ3ሻ . What does it mean in this context?  \n􀝂ሺ3ሻ ൌ 24 3 hours after 8:00 (or 11:00), the patients insulin level is 24 mclU/ml.  \nd. Find average rate of change from [0, 3] . Explain the meaning in this context.  \nTime since 8:00 (hours)  \nଶସି଼ ൌ ଵ଺ ൌ 5.333  \nଷି଴ ଷ The patient’s insulin level increased 5.333 levels every hour for the first 3 hours.  \n© The Algebros [from FlippedMath.com](from FlippedMath.com)  \n1.13 Function Model Selection  1.13 Test Prep   Multiple Choice-CALCULATOR ACTIVE  \nFor questions 9 and 10, use the table of values for polynomial f at selected values of x.  \n\n| 􀢞 | 2 | 4 | 6 | 8 | 10 | 12 |\n| --- | --- | --- | --- | --- | --- | --- |\n| 􀢌ሺ􀢞ሻ | 97 | 405 | 977 | 1861 | 3105 | 4757 |\n\n9. Which of the following statements are true ?  \n(A) The function is quadratic because second differences are a nonzero constant  \n(B) The function is quadratic because third differences are a nonzero constant  \n(C) The function is cubic because second differences are a nonzero constant  \n(D) The function is cubic because third differences are a nonzero constant  \n10. The average rate of change from 􀝔 ൌ െ 22 to 􀝔 ൌ 4 is 34. Which statement best ","cbCaimPa8g5t4swE","https://ap.wps.com/l/cbCaimPa8g5t4swE","pdf",757415,"English","# 1.13 Function Model Selection\n## Practice Problems\n## Multiple Choice","[{\"question\":\"How do you determine whether data is modeled by a linear, quadratic, or cubic function?\",\"answer\":\"Use finite differences: constant first differences indicate linear, constant second differences indicate quadratic, and constant third differences indicate cubic. The practice section explicitly links each answer choice to the relevant nonzero constant difference level.\"},{\"question\":\"In the painkiller problem, how do you interpret f(2) and the average rate of change from t=1 to t=2?\",\"answer\":\"Evaluate the function at the given time to get the amount in the bloodstream at that hour. Compute the average rate of change between the two times to find how fast the amount is leaving the bloodstream over that interval, explained in context as a per-hour change.\"},{\"question\":\"How are the domain and range handled for the rectangle-in-a-circle and the strawberry/insulin piecewise contexts?\",\"answer\":\"For the rectangle area function, the restricted domain is based on the rectangle width limits from the circle diameter, and the restricted range covers achievable areas. For strawberries and insulin, domain reflects allowed quantities/time and range reflects feasible prices or insulin levels, with explanations tied to context.\"}]","1.13 Function Model Selection - Practice | PDF"]