[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-665529-105":59,"doc-detail-665529-en":134},{"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":127,"head_meta":129,"extra_data":131,"updated_unix":133},105,"en","s4-new-curriculum-o-level-mathematics-chapter-1-composite-functions","S4 New Curriculum O-level mathematics - Chapter 1 - Composite functions","","Term 1 Theme: Patterns and Algebra introduces Chapter 1 on composite functions through foundational ideas of relations and mappings. It explains ordered pairs, domain and range, and shows relations represented by tables, graphs, and mapping diagrams. The material distinguishes relations from functions, including one-to-one, many-to-one, one-to-many, and many-to-many cases, and connects mappings to real-life examples. It further develops function notation, evaluation steps, and practice questions involving different input substitutions and algebraic function forms.",{"@graph":69,"@context":126},[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/s4-new-curriculum-o-level-mathematics-chapter-1-composite-functions/665529/",{"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/s4-new-curriculum-o-level-mathematics-chapter-1-composite-functions/665529.png","ImageObject",300,407,{"name":92,"@type":93},"lilac","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118,122],{"name":109,"@type":110,"acceptedAnswer":111},"What is a relation, and what are domain and range?","Question",{"text":112,"@type":113},"A relation is a set of ordered pairs showing how elements from one set (the domain) are connected to elements in another set (the range).","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"When is a mapping diagram considered a function?",{"text":117,"@type":113},"A mapping diagram is a function only if each input value in the domain is paired with exactly one output value in the range.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you evaluate a function using function notation like f(x)?",{"text":121,"@type":113},"Substitute the input value into the function, perform the operations, and the result is the output f(x).",{"name":123,"@type":110,"acceptedAnswer":124},"What practice skills does Chapter 1 focus on besides definitions?",{"text":125,"@type":113},"It focuses on drawing mapping diagrams for given domains and rules, and evaluating or solving for unknowns using function notation with substitution.","https://schema.org",{"og:url":83,"og:type":128,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":130,"canonical":83},"index,follow",{"doc_id":132,"site_id":62},665529,1793304739,{"code":4,"msg":5,"data":135},{"doc_id":132,"user_id":136,"nickname":92,"user_avatar":137,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":138,"file_id":139,"file_url":140,"file_type":141,"file_size":142,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"language":143,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":144,"faqs":145,"seo_title":146,"seo_description":67,"update_tm":133,"read_time":147},3985747861865,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","S4 New Curriculum O-level mathematics Term 1  \nTheme: Patterns and Algebra  \nChapter 1: Composite functions  \nRelation  \nA relation is a set of ordered pairs that showshow elements from one set (called the domain) are connected to elements in another set (called the range) .  \n􀁸 Example: If Set A = {1, 2, 3} and Set B = {4, 5, 6}, a relation could be: R = {(1, 4),(2, 5),(3, 6)}  \n􀁸 Relations can be represented as:  \no Ordered pairs  \no Tables  \no Graphs  \no Mapping diagrams  \nA mapping is a visual or formal way to show how each element in the domain is paired with an element in the range. It’s often used to describe functions, which are special types of relations.  \n􀁸 A function is a mapping where each input has exactly one output.  \n􀁸 Not all mappings are functions, but all functions are mappings.  \nTypes of Relations  \n\n| Type | Description |\n| --- | --- |\n| One-toOne | Each element in the domain maps to a unique element in the range |\n| Many-toOne | Multiple domain elements map to the same range element |\n| One-toMany | A domain element maps to multiple range elements (not a function) |\n| Many-toMany | Multiple domain elements map to multiple range elements (not a function) |\n\nMapping Diagram  \nA mapping diagram is a visual tool used in mathematics to show how elements from one set (called the domain) are paired with elements from another set (called the range) . Lines are drawn to match each item/element in the domain with its corresponding  \nitem/element in the range.  \nExample 1  \nDraw a mapping diagram in which Capital cities are mapped to the Countries of East Africa  \nmeans that  \nKampala is the capital city of Uganda, that is why Kampala is mapped to Uganda  \nMapping function  \nA mapping function in mathematics is a special kind of relation that pairs each element from one set (called the domain) with exactly one element from another set (called the range) .  \nA mapping diagram is a function only if each input value is paired with one output value, for instance below, relations A and B are functions because each input is mapped to one output while C is not because one of the inputs is mapped to more than one output.  \nReal-Life Applications of Mappings and Relations  \n1. Education: Students and Grades  \n􀁸 Each student is related to their grades in different subjects.  \n􀁸 This is a relation: {(Alice, A),(Bob, B),(Charlie, A)}  \n2. Temperature and Time  \n􀁸 The temperature at different times of the day forms a relation: {(8 AM, 70°F),(12 PM, 85°F),(6 PM, 75°F)}  \n􀁸 This is a function since each time has one temperature reading.  \n3. Fuel Cost and Quantity  \n􀁸 The cost of fuel is a function of the number of liters purchased: {(10 L, sh. 2000),(20 L, sh. 4000)}  \n􀁸 This is a function because each quantity has one cost.  \n4. Family Relationships  \n􀁸 Parent-child or sibling relationships are relations: {(John, Mike), (Sarah, Anna)}  \n5. Library Systems  \n􀁸 Books and borrowers form a relation:{(Book 1, Borrower A),(Book 2, Borrower B)}  \n􀁸 A book can be borrowed by multiple people—not a function.  \n6. Shopping: Items and Prices  \n􀁸 Each item has a price, forming a function: {(Milk, sh. 2500),(Bread, sh. 5000), (Eggs, sh. 500)}  \n7. Taxi Fare and Time  \n􀁸 Fare is a function of time spent in the taxi—more time, higher cost.  \n8. Age and Height  \n􀁸 For a group of people, age and height form a relation.  \n􀁸 For one person, height over time is a function of age.  \n9. Velocity in Physics  \n􀁸 Velocity of a falling object is a function of time: v(t) = 9 .8t (ignoring air resistance)  \n10. ATM Withdrawals  \n􀁸 The amount dispensed is a function of the amount requested—one input, one output  \nTrial 1  \n1. Draw mapping diagrams for the domain {0, 1, 2, 3, 4} to their  \n(a) Squares  \n(b) Cubes  \n2. Draw an arrow diagram representing the following mapping using the given domain  \n(a) Domain{2, 3, 4, 5} for x → 3x + 2  \n(b) Domain (1, 2, 6, 8} for x → x2 + 1  \n(c) Domain {0, 2, 3, 5} for x → 2x3-x  \n(d) Domain {1, 3, 5, 7, 11} for x → 5x-5","cbCaiedcryxVJrK5","https://ap.wps.com/l/cbCaiedcryxVJrK5","pdf",952897,"English","# Relation\n## Examples and representations\n# Types of relations\n# Mapping diagram and mapping function\n## Function conditions\n# Real-life applications of mappings and relations\n# Function notation\n## Evaluating functions\n# Practice (Trial questions)","[{\"question\":\"What is a relation, and what are domain and range?\",\"answer\":\"A relation is a set of ordered pairs showing how elements from one set (the domain) are connected to elements in another set (the range).\"},{\"question\":\"When is a mapping diagram considered a function?\",\"answer\":\"A mapping diagram is a function only if each input value in the domain is paired with exactly one output value in the range.\"},{\"question\":\"How do you evaluate a function using function notation like f(x)?\",\"answer\":\"Substitute the input value into the function, perform the operations, and the result is the output f(x).\"},{\"question\":\"What practice skills does Chapter 1 focus on besides definitions?\",\"answer\":\"It focuses on drawing mapping diagrams for given domains and rules, and evaluating or solving for unknowns using function notation with substitution.\"}]","S4 New Curriculum O-level mathematics - Chapter 1 - Composite functions | PDF",18]