{"id":5149,"date":"2023-06-27T12:08:26","date_gmt":"2023-06-27T12:08:26","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=5149"},"modified":"2025-08-28T03:31:01","modified_gmt":"2025-08-28T03:31:01","slug":"math-in-arts-background-youll-need-2","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/math-in-arts-background-youll-need-2\/","title":{"raw":"Math in Arts: Background You'll Need 2","rendered":"Math in Arts: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Identify how functions flip<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Vertical Reflection<\/h2>\r\n<p>Another transformation that can be applied to a function is a reflection over the [latex]x[\/latex]- or [latex]y[\/latex]-axis. A <strong>vertical reflection<\/strong> reflects a graph vertically across the [latex]x[\/latex]-axis, while a <strong>horizontal reflection<\/strong> reflects a graph horizontally across the [latex]y[\/latex]-axis. The reflections are shown in the figure below.<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18203556\/CNX_Precalc_Figure_01_05_0122.jpg\" alt=\"Graph of the vertical and horizontal reflection of a function.\" width=\"487\" height=\"442\" \/> Figure 1. Vertical and horizontal reflections of a function[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>Notice that the vertical reflection produces a new graph that is a mirror image of the base or original graph about the [latex]x[\/latex]-axis. The horizontal reflection produces a new graph that is a mirror image of the base or original graph about the [latex]y[\/latex]-axis.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>vertical reflection<\/h3>\r\n\r\nGiven a function [latex]f\\left(x\\right)[\/latex], a new function [latex]g\\left(x\\right)=-f\\left(x\\right)[\/latex] is a <strong>vertical reflection<\/strong> of the function [latex]f\\left(x\\right)[\/latex], sometimes called a reflection about (or over, or through) the [latex]x[\/latex]-axis.<\/div>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]8814[\/ohm2_question]<\/section>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>horizontal reflection<\/h3>\r\n\r\nGiven a function [latex]f\\left(x\\right)[\/latex], a new function [latex]g\\left(x\\right)=f\\left(-x\\right)[\/latex] is a <strong>horizontal reflection<\/strong> of the function [latex]f\\left(x\\right)[\/latex], sometimes called a reflection about the [latex]y[\/latex]-axis.<\/div>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]8815[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Identify how functions flip<\/li>\n<\/ul>\n<\/section>\n<h2>Vertical Reflection<\/h2>\n<p>Another transformation that can be applied to a function is a reflection over the [latex]x[\/latex]&#8211; or [latex]y[\/latex]-axis. A <strong>vertical reflection<\/strong> reflects a graph vertically across the [latex]x[\/latex]-axis, while a <strong>horizontal reflection<\/strong> reflects a graph horizontally across the [latex]y[\/latex]-axis. The reflections are shown in the figure below.<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 487px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18203556\/CNX_Precalc_Figure_01_05_0122.jpg\" alt=\"Graph of the vertical and horizontal reflection of a function.\" width=\"487\" height=\"442\" \/><figcaption class=\"wp-caption-text\">Figure 1. Vertical and horizontal reflections of a function<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Notice that the vertical reflection produces a new graph that is a mirror image of the base or original graph about the [latex]x[\/latex]-axis. The horizontal reflection produces a new graph that is a mirror image of the base or original graph about the [latex]y[\/latex]-axis.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>vertical reflection<\/h3>\n<p>Given a function [latex]f\\left(x\\right)[\/latex], a new function [latex]g\\left(x\\right)=-f\\left(x\\right)[\/latex] is a <strong>vertical reflection<\/strong> of the function [latex]f\\left(x\\right)[\/latex], sometimes called a reflection about (or over, or through) the [latex]x[\/latex]-axis.<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm8814\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=8814&theme=lumen&iframe_resize_id=ohm8814&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>horizontal reflection<\/h3>\n<p>Given a function [latex]f\\left(x\\right)[\/latex], a new function [latex]g\\left(x\\right)=f\\left(-x\\right)[\/latex] is a <strong>horizontal reflection<\/strong> of the function [latex]f\\left(x\\right)[\/latex], sometimes called a reflection about the [latex]y[\/latex]-axis.<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm8815\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=8815&theme=lumen&iframe_resize_id=ohm8815&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":16,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":91,"module-header":"background_you_need","content_attributions":[{"type":"original","description":"Revision and Adaptation","author":"","organization":"Lumen Learning","url":"","project":"","license":"cc-by","license_terms":""},{"type":"cc","description":"College Algebra","author":"Abramson, Jay et al.","organization":"OpenStax","url":"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2","project":"","license":"cc-by","license_terms":"Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2"}],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/5149"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/16"}],"version-history":[{"count":17,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/5149\/revisions"}],"predecessor-version":[{"id":15782,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/5149\/revisions\/15782"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/91"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/5149\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=5149"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=5149"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=5149"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=5149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}