[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-538024-105":59,"doc-detail-538024-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","mathematics-grade-8-functions-sample-items-to-success","MATHEMATICS GRADE 8 - Functions - Sample Items to Success","","Mathematics Grade 8 functions sample items focus on identifying whether a relation is a function, distinguishing function versus non-function behavior using tables and input-output evidence. Tasks include determining if a function is one-to-one, evaluating functions from equations, completing tables, and interpreting graphs on a coordinate plane. Additional items compare two linear functions by slope and y-intercept, analyze domain and range, and decide where functions increase or decrease, using reasoning aligned with proficiency expectations.",{"@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/mathematics-grade-8-functions-sample-items-to-success/538024/",{"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/mathematics-grade-8-functions-sample-items-to-success/538024.png","ImageObject",300,407,{"name":92,"@type":93},"hdkawk","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-10",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you provide evidence that a relation is not a function?","Question",{"text":112,"@type":113},"You identify an input that fails the function rule, such as when one output is produced by more than one input (or when an input does not have exactly one output, depending on the item).","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does it mean for a one-to-one function, and how can you check it?",{"text":117,"@type":113},"A one-to-one function requires that different inputs lead to different outputs. Check this using a table or mapping by verifying that no two inputs produce the same output.",{"name":119,"@type":110,"acceptedAnswer":120},"How can you compare two linear functions using slope and y-intercept?",{"text":121,"@type":113},"Compare the y-intercept values to determine which functions share the same intercept. Compare slopes (rate of change) to decide which function increases faster and how the graphs differ.","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},538024,1791753761,{"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":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":41,"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":144,"preview_page_count":4},3985747859855,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Samples to Success  \nSample items provide valuable insight into how students engage with different texts, tasks, and contexts, highlighting the types of opportunities they need for success in the classroom. These items offer a shared reference point for understanding proficiency expectations, complementing the assessment's role in measuring learning. By analyzing items alongside performance data, educators can gain a deeper understanding of students' strengths and areas for growth. Students thrive in environments rich with diverse materials, challenges that vary in task type, and multiple avenues for demonstrating understanding. High-quality instruction, aligned with the learning goals, is the most effective way to support students'growth and prepare them for success.  \nThe items featured in this rubric are a mix of items representative of those found on the Illinois Assessment of Readiness (IAR) and items appropriate for classroom instruction to support and build the skills measured on the IAR. The distinction between a student scoring proficient and above proficient on the IAR is primarily determined by the total points earned on items that require modeling and/or reasoning. Students who can effectively explain and demonstrate their thinking are most likely to earn these points.  \nMATHEMATICS GRADE 8  \nFunctions  \nThe table shows a relation.  \nThe relation is not a function. Which input provides evidence that the relation is not a function?  \nA. -1  \nB. 3  \nC. 1  \nD. -2  \nThe table shows a relation.  \nWhich statement about the relation is correct?  \nA. The relation is a function because each input has exactly one output.  \nB. The relation is a function because each output has exactly one input.  \nC. The relation is not a function  \none output.  \nD. The relation is not a function because one output has more than one input.  \nThe table shows a relation.  \n\n| 4 | 4 |\n| --- | --- |\n\nIs the relation a function? Answer: yes  \nIf not, explain why not?  \nIf so, is it a one-to-one function? Explain why or why not.  \nThe relation is not a one-to-one function because an input of 3 and an input of 4 both result in an output of 4.  \nApproaching Proficient  \nProficient  \nAbove Proficient  \nExpectation at Proficient:  \nDetermine whether a relation is a function.  \nbecause one input has more than  \n\n| Input | Output |\n| --- | --- |\n| 1 | 2 |\n| 2 | 3 |\n| 3 | 4 |\n\nFunctions  \nExpectation at Proficient:  \nGraph the set of ordered pairs consisting of an input and the corresponding output.  \nA coordinate plane and points A, B, and C are shown.  \nComplete the table of input and output values for the points A, B, and C.  \nA coordinate plane and points A, B, and C are shown.  \nComplete the table of input and output values for the points A, B, and C.  \nA table of input and output values for a relation is shown.  \nGraph the set of ordered pairs in the table on a coordinate plane.  \nA function is shown.  \n􀝂 (􀝔) = 2􀝔2 + 3 Evaluate the function for the following inputs values.  \n􀝂 (1) =    \n􀝂 (2) =    \n􀝂 (−2) =   Answers:  \n1) 2)−2)  \n8.F.1-2  \nBelow Proficient  \nApproaching Proficient  \nProficient  \nAbove Proficient  \n􀝂 ( = 5  \n􀝂 ( = 11  \n􀝂 ( = 11  \n| Point | Input | Output |\n| --- | --- | --- |\n| A | -3 | \u003Cbr>2 |\n| B | \u003Cbr>1 | 3 |\n| C | 4 | \u003Cbr>0 |\n\n\n| Point | Input | Output |\n| --- | --- | --- |\n| A | -3 | \u003Cbr>2 |\n| B | \u003Cbr>1 | \u003Cbr>3 |\n| C | 4 | \u003Cbr>0 |\n\nFunctions  \n8. F.2 Below Proficient  \nTwo linear functions are shown. Two linear functions are shown. Two linear functions are shown. Two linear functions are shown.  \nWhich function has the greater output when the input is 2?  \nAnswer: Function 2  \nWhich function has the greater yintercept?  \nA. Function 1  \nB. Function 2  \nC. Neither, both have a y-intercept of (0,2)  \nD. Neither, both have a y-intercept of (0,1)  \nWhich function has the higher rate of change? Explain how you know.  \nFunction 2; The slope of Function 1 is 43while the slope of Function 2 is  \n.  \nGraph each function on the same coor","cbCaibDMt3m8Opd2","https://ap.wps.com/l/cbCaibDMt3m8Opd2","pdf",1454074,"English","# Functions\n## Determine whether a relation is a function\n## One-to-one function reasoning\n## Graphing and evaluating functions\n## Linear functions: slope and y-intercept\n## Domain, range, and increasing/decreasing intervals","[{\"question\":\"How do you provide evidence that a relation is not a function?\",\"answer\":\"You identify an input that fails the function rule, such as when one output is produced by more than one input (or when an input does not have exactly one output, depending on the item).\"},{\"question\":\"What does it mean for a one-to-one function, and how can you check it?\",\"answer\":\"A one-to-one function requires that different inputs lead to different outputs. Check this using a table or mapping by verifying that no two inputs produce the same output.\"},{\"question\":\"How can you compare two linear functions using slope and y-intercept?\",\"answer\":\"Compare the y-intercept values to determine which functions share the same intercept. Compare slopes (rate of change) to decide which function increases faster and how the graphs differ.\"}]","MATHEMATICS GRADE 8 - Functions - Sample Items to Success | PDF",1791606013,76]