[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-573096-105":53,"doc-detail-573096-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","graphing-transformations-cheat-sheet","Graphing Transformations - Cheat Sheet","","This document serves as a concise study guide and cheat sheet for understanding mathematical graphing transformations. It provides a structured breakdown of vertical and horizontal translations, illustrating how adding or subtracting values from a function affects its position on a coordinate plane. Specifically, it details shifts for absolute value functions, differentiating between upward, downward, leftward, and rightward movements. Designed for students, this resource simplifies complex algebraic concepts into quick, actionable references for reviewing function behavior and graphical representation changes. By categorizing translations and referencing visual patterns, the guide aids in the rapid retention of essential calculus and algebra principles required for academic success in mathematics. It emphasizes the practical application of functional changes, making it an indispensable tool for learners seeking to master coordinate geometry and function sketching efficiently.",{"@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":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/graphing-transformations-cheat-sheet/573096/",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/graphing-transformations-cheat-sheet/573096.png","ImageObject",442,249,{"name":88,"@type":89},"Kyle","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-18","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":76},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"How does a vertical translation occur in a function?","Question",{"text":108,"@type":109},"Vertical translations are achieved by adding or subtracting a value from the output of the function f(x), such as f(x) + 10 for an upward shift or f(x) - 10 for a downward shift.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"What is the effect of changing the input in a horizontal translation?",{"text":113,"@type":109},"Horizontal translations are created by modifying the input of the function, such as f(x+10) which shifts the graph to the left, or f(x-10) which shifts the graph to the right.",{"name":115,"@type":106,"acceptedAnswer":116},"What concepts are covered in this cheat sheet?",{"text":117,"@type":109},"This cheat sheet covers the rules for vertical and horizontal translations of graphs, along with brief references to stretches and shrinks.","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},573096,1792087352,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":76,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":9,"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":4},3985741905716,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Graphing Transformations Cheat Sheet  \n[by](by blueberryshortcake via cheatography.com/162779/cs/34074/)[ blueberryshortcake](by blueberryshortcake via cheatography.com/162779/cs/34074/)[ via](by blueberryshortcake via cheatography.com/162779/cs/34074/)[ cheatography.com/162779/cs/34074/](by blueberryshortcake via cheatography.com/162779/cs/34074/)  \nTranslations  \n\n| Vertical --added | Horizontal -- |\n| --- | --- |\n| value does not affect | added value affect |\n| input | input |\n| f(x) = |x |+10 shifts UP | f(x) = |x+10| shifts LEFT |\n| f(x) = |x |-10 shifts | f(x) = |x-10| shifts |\n| DOWN | RIGHT |\n| Translations (visual) |  |\n| \u003Cbr>Stretches & Shrinks |  |\n| \u003Cbr>Stretches | \u003Cbr>Shrinks |\n\nBy blueberryshortcake  \n[cheatography.com/blueberryshortcake/](cheatography.com/blueberryshortcake/)  \nNot published yet.  \nLast updated 8th September, 2022. Page 1 of 1.  \nSponsored by Readable.com Measure your website readability!  \n[https://readable.com](https://readable.com)","cbCaiuPC43bgbBzB","https://ap.wps.com/l/cbCaiuPC43bgbBzB","pdf",110107,"English","# Translations\n## Vertical Shifts\n## Horizontal Shifts","[{\"question\":\"How does a vertical translation occur in a function?\",\"answer\":\"Vertical translations are achieved by adding or subtracting a value from the output of the function f(x), such as f(x) + 10 for an upward shift or f(x) - 10 for a downward shift.\"},{\"question\":\"What is the effect of changing the input in a horizontal translation?\",\"answer\":\"Horizontal translations are created by modifying the input of the function, such as f(x+10) which shifts the graph to the left, or f(x-10) which shifts the graph to the right.\"},{\"question\":\"What concepts are covered in this cheat sheet?\",\"answer\":\"This cheat sheet covers the rules for vertical and horizontal translations of graphs, along with brief references to stretches and shrinks.\"}]","Graphing Transformations - Cheat Sheet | PDF",1791932207]