[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-573098-105":53,"doc-detail-573098-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","edexcel-igcse-maths-transformations-of-graphs-translations-reflections","Edexcel IGCSE Maths - Transformations of Graphs - Translations & Reflections","","Edexcel IGCSE Maths revision notes explain graph transformations with a focus on translations, reflections, and how to interpret them in function notation. A translation is described using y = f(x + a) and y = f(x) + b, including sign changes and direction along the x- and y-axes. Reflections are explained via y = f(-x) and y = -f(x), linking negative terms to reflections in the x-axis or y-axis. Worked examples guide how to sketch the transformed graphs.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/edexcel-igcse-maths-transformations-of-graphs-translations-reflections/573098/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/edexcel-igcse-maths-transformations-of-graphs-translations-reflections/573098.png","ImageObject",442,249,{"name":88,"@type":89},"WPS_1786070896","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-19","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":79},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"How do you identify a translation from function notation?","Question",{"text":108,"@type":109},"For y = f(x + a), the value a inside the bracket translates the graph by −a along the x-axis. For y = f(x) + b, the value b outside the bracket translates the graph by +b along the y-axis, with sign changes determining direction.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"What do y = f(-x) and y = -f(x) mean for reflections?",{"text":113,"@type":109},"y = f(-x) reflects the graph in the y-axis (left/right). y = -f(x) reflects the graph in the x-axis (up/down) by reversing the sign of all y-coordinates.",{"name":115,"@type":106,"acceptedAnswer":116},"When given a transformed function, how should you sketch the new graph?",{"text":117,"@type":109},"Copy the original graph into its new position. Translate key points like endpoints and vertices first, then join them with straight lines to form the transformed graph.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},573098,1792241639,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":79,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":45,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":140},549768072016,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Head to www.savemyexams. com for more awesome resources  \n Edexcel IGCSE Maths  \nTransformations of Graphs  \nContents  \n Translations of Graphs  Re}ections of Graphs  Stretches of Graphs  \nPage 1 of 21  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nTranslations of Graphs  \nGraph Transformations What are graph transformations?  \n A transformation is simply a change of some sort  \n Re}ections (using either the x-axis or y-axis as a mirror line)  \n Translations (moving the whole graph inthex and/or y direction)  \n Stretches (enlarging the graph but only in thex direction or only in they direction)  \n You should be able to recognise these three diyerent methods of transforming graphs and be able to apply them to a given graph  \nPage 2 of 21  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nTranslations of Graphs  \nHow do we translate the graphofa function? Given a transformation in function notation, then  \n y = f(x + a) represents a translation − a units in thex axis  \n a is inside the bracket  \n Note the change of sign highlighted!  \n y = f(x) + b represents a translation + b units in they direction  \n a is outside the bracket  \n For example, y = f(x + 3) + 2 means  \n a translation of y = f(x) by −3 in x the direction and +2 in they direction  \n Note the change of sign inthex direction as pointed out above! How do we describe translations of graphs?  \n Some questions give a transformed function in the formy = f(x + a) or y = f(x) + a and askyouto describe the transformation  \n To describe a translation fully, you must include;􀂋 . the transformation: \"translation\"  \n􀂌 . the direction in thex-axis and in they-axis  \n this can be given as a worded description, e. g. \" 3 left and 2 up \" / \" −3 inthex-axis and +2 in they-axis \"  \n⎜⎛ x ⎞⎟ ⎜⎛ −3 ⎞⎟  \n or it can be given as a vector  y ⎠⎟ , e. g. \" by  2 ⎠⎟ \"  \n Remember that  \n if the a is inside the bracket, its a translation by − a in the x-axis  \n if the a is outside the bracket, its a translation by a in they-axis  \n Examiner Tip REMEMBER that;  \n y = f(x + a); \" a \" next to x, translates in x-axis by − a  \n y = f(x) + a; \" a \" not next to x, translates in y-axis  \nPage 3 of 21  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \n\n|  Worked example\u003Cbr>The graphof y = f( x) is shown on the graph below.\u003Cbr>On the same graph sketchy = f( x + 3) + 2 . |\n| --- |\n| |\n| This is a translation by −3 in thex direction (i. e. 3 to the left, note the change of sign again) and +2 in they direction (i. e. 2 up)\u003Cbr>So we copy the given graph in its new position. Translate key points-endpoints and vertices like the vertex shown below- |rst, then join the points with straight lines\u003Cbr>Page 4 of 21\u003Cbr>© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers |\n\nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nPage 5 of 21  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \n Worked example  \nDescribe the transformation that maps the graphofy = f( x) to the graphof y = f( x − 4) − 6 .  \nThe number inside the bracket (next to x) is −4 so this is a translation by +4 inthex-axis (note the change in sign again)  \nThe number outside the bracket (not next to x!) is −6 so this is a translation by −6 in they-axis  \nTranslation by  \nor Translation 4 right and 6 down or Translation by +4 inthex-axis and − 6 in they-axis  \nPage 6 of 21  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nRe}ections of Graphs  \nRe}ections of Graphs  \nHow do were}ect grap","cbCaifDoWNPRey57","https://ap.wps.com/l/cbCaifDoWNPRey57","pdf",2907349,"English","# Transformations of Graphs\n## Translations of Graphs\n## Re}ections of Graphs\n## Worked examples\n## Functions in transformation notation","[{\"question\":\"How do you identify a translation from function notation?\",\"answer\":\"For y = f(x + a), the value a inside the bracket translates the graph by −a along the x-axis. For y = f(x) + b, the value b outside the bracket translates the graph by +b along the y-axis, with sign changes determining direction.\"},{\"question\":\"What do y = f(-x) and y = -f(x) mean for reflections?\",\"answer\":\"y = f(-x) reflects the graph in the y-axis (left/right). y = -f(x) reflects the graph in the x-axis (up/down) by reversing the sign of all y-coordinates.\"},{\"question\":\"When given a transformed function, how should you sketch the new graph?\",\"answer\":\"Copy the original graph into its new position. Translate key points like endpoints and vertices first, then join them with straight lines to form the transformed graph.\"}]","Edexcel IGCSE Maths - Transformations of Graphs - Translations & Reflections | PDF",1791932207,7]