[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-665530-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-665530-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":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","linear-focus-mapping-diagrams-and-fixed-points","Linear Focus - Mapping Diagrams and Fixed Points","","Works through linear functions using linear focus points to construct and interpret mapping diagrams. Includes completing tables and mapping diagrams for a given function, sketching graphs with appropriate axis scales, and analyzing linear equations by finding where function values coincide. Covers fixed points by solving f(x)=x, builds composite mapping diagrams for function compositions, and extends to inverse linear functions using transparency-style diagram flipping. Discusses how axis scale choices affect focus point positions and equation solving.",{"@graph":14,"@context":72},[15,34,55],{"@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/linear-focus-mapping-diagrams-and-fixed-points/665530/",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/linear-focus-mapping-diagrams-and-fixed-points/665530.png","ImageObject",300,407,{"name":42,"@type":43},"BigDaveOnline","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":52,"interactionType":53,"userInteractionCount":22},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"How do you complete a mapping diagram for a linear function like f(x)=5x−7?","Question",{"text":62,"@type":63},"Compute target values for each given x, then choose a matching vertical-axis scale and plot arrows from each x to its corresponding f(x) value. Use the chart to sketch the graph if required.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How does the linear focus point help solve an equation such as f(x)=g(x)?",{"text":67,"@type":63},"For each function, find its focus point, then use the focus points to determine solutions. Visually, identify where the mapping behaviors coincide to get the x-value(s) satisfying f(x)=g(x).",{"name":69,"@type":60,"acceptedAnswer":70},"What role do axis scales play when using the focus point to solve equations?",{"text":71,"@type":63},"The choice of vertical and horizontal scales changes the plotted position of the focus point on the diagram, which affects how you read and use it to solve equations. The underlying solution x-values come from the consistent visual relationship created by the chosen scales.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},665530,1793304740,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"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":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"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":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":100,"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":79,"read_time":143},962090896214,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","1. Suppose that f (x) = 5x – 7 for all x 0ú .  \na. Complete the following table :  \n\n| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| f(x) |  |  |  |  |  |  |  |\n\nb. Complete the following mapping diagram for f with the indicated numbers (determine an appropriate scale for the target values.):  \nc. Sketch a graph forf based on the chart (determine an appropriate scale for the vertical axis.):  \n2. Let f (x) = mx + b sketch mapping diagrams for the following:  \nUse the same scale for the second axis.  \na. m = -2 ; b = 1 : f (x) = -2x + 1 m = 2;  \nb. b = 1 : f (x) = 2x + 1  \nc. m = ½ ; b = 1:f (x) = ½ x + 1  \nd. m = 0 ; b = 1:f (x) = 0 x + 1  \ne. m = 1 ; b = 1 : f (x) = x + 1  \n3. Using the focus point to solve a problem. [Use the same scale for the second axis.]  \nE 1.Solving a linear equation: 2x+1 =5 ; 2x+1 = x + 2 Let f(x) = 2x+1 and g(x) = x+2  \nFor which x does f(x) = 5; f(x) = g(x)?  \nSolution: Find the focus points [2,1] for f and [1,2] for g. Use [2,1] and [1,2] to find the solutions.  \nWhat visual feature of [2,1] and [1,2] identified x where f(x) = g(x)?  \n4. Find “fixed points” off :f (x) = 2x+1 For which x does f (x) = x?  \nSolution: Find the focus point [2,1] for f. Use [2,1] to find the solution. What visual feature of [2, 1] identified x where f (x) = x?  \n5.  \na. On separate diagrams sketch mapping diagrams for g(x) = 2x and h(x)= x+1  \nb. Use these sketches to draw a composite sketch of the mapping diagram for the composite  \nfunction f(x) = h(g(x)) =(2x) + 1 and then  \na sketch for the mapping diagram off(x) = 2 x + 1  \nc. Use the sketches of part a. to draw a composite sketch of the mapping diagram for the composite function p(x) = g(h(x)) =2(x + 1) and then a sketch for the mapping diagram of p(x) = 2(x + 1) = 2x +2  \nInverse linear functions:  \n6.  \na. Make a transparency for mapping diagrams for g(x) = 2x and h(x)= x + 1. Flip the transparency over and use this on separate diagrams to sketch mapping diagrams for  \ninvg(x) = 1/2 x and Invh(x)= x-1  \n“Socks and shoes” with mapping Diagrams  \nb. Use the sketches of part a to draw a composite sketch of the mapping diagram for the composite function invf(x) = invh(invg(x)) =1/2(x-1) and then a sketch for the mapping diagram of invf(x) = 1/2(x-1) = 1/2x-1/2  \n7. How would you use the Linear Focus to find the mapping diagram for the function inverse for a linear function when m 􀂅 ?0?  \n8. How does the choice of axis scales affect the position of the linear function focus point and its use in solving equations?","cbCairUxytGM91Q9","https://ap.wps.com/l/cbCairUxytGM91Q9","pdf",162796,"English","# Mapping diagrams for linear functions\n## Completing tables and mapping diagrams\n## Sketching graphs with axis scales\n# Using linear focus to solve equations\n## Solving f(x)=g(x)\n## Fixed points where f(x)=x\n# Composite and inverse mapping diagrams\n## Compositions h(g(x)) and g(h(x))\n## Inverse functions via flipped mapping diagrams\n## Axis scale effects on focus points","[{\"question\":\"How do you complete a mapping diagram for a linear function like f(x)=5x−7?\",\"answer\":\"Compute target values for each given x, then choose a matching vertical-axis scale and plot arrows from each x to its corresponding f(x) value. Use the chart to sketch the graph if required.\"},{\"question\":\"How does the linear focus point help solve an equation such as f(x)=g(x)?\",\"answer\":\"For each function, find its focus point, then use the focus points to determine solutions. Visually, identify where the mapping behaviors coincide to get the x-value(s) satisfying f(x)=g(x).\"},{\"question\":\"What role do axis scales play when using the focus point to solve equations?\",\"answer\":\"The choice of vertical and horizontal scales changes the plotted position of the focus point on the diagram, which affects how you read and use it to solve equations. The underlying solution x-values come from the consistent visual relationship created by the chosen scales.\"}]","Linear Focus - Mapping Diagrams and Fixed Points | PDF",15]