{"id":471,"date":"2025-07-10T16:41:55","date_gmt":"2025-07-10T16:41:55","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=471"},"modified":"2025-12-22T17:06:58","modified_gmt":"2025-12-22T17:06:58","slug":"introduction-to-functions-background-youll-need-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/introduction-to-functions-background-youll-need-3\/","title":{"raw":"Introduction to Functions: Background You'll Need 3","rendered":"Introduction to Functions: Background You&#8217;ll Need 3"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Recognize positive, negative, and zero slope<\/li>\r\n<\/ul>\r\n<\/section><section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\r\n<h3>sign of slope<\/h3>\r\n<p class=\"whitespace-normal break-words\">The sign of a slope tells us the direction a line moves:<\/p>\r\n\r\n<ul class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-disc space-y-1.5 pl-7\">\r\n \t<li class=\"whitespace-normal break-words\">Positive slope: Line rises from left to right<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Negative slope: Line falls from left to right<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Zero slope: Line is horizontal<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Undefined slope: Line is vertical<\/li>\r\n<\/ul>\r\n<img src=\"https:\/\/openstax.org\/apps\/image-cdn\/v1\/f=webp\/apps\/archive\/20250522.165258\/resources\/40350686e52f6175268fa33a48576e28e387a022\" alt=\"The image shows four arrows. The first arrow is slanted and pointing up and to the right and is labeled \u201cpositive\u201d. The second arrow is slanted and pointing down and to the right and labeled \u201cnegative\u201d. The third arrow is horizontal and labeled \u201czero\u201d. The fourth arrow is vertical and labeled \u201cundefined\u201d.\" \/>\r\n\r\n<\/section><section class=\"textbox recall\" aria-label=\"Recall\">For lines given in the form [latex]y=mx+b[\/latex], slope is [latex]m[\/latex], the coefficient of [latex]x[\/latex].<\/section><section class=\"textbox example\" aria-label=\"Example\">Identify the type of slope for each scenario:a)<img src=\"https:\/\/openstax.org\/apps\/image-cdn\/v1\/f=webp\/apps\/archive\/20250522.165258\/resources\/d17d908fe193fcd7fdb1e0872ae05773588f142f\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, negative 2) and (3, 3).\" \/>b)<img src=\"https:\/\/openstax.org\/apps\/image-cdn\/v1\/f=webp\/apps\/archive\/20250522.165258\/resources\/fff70f8e7e94cf3dfa4eb66a0cc94a2abbdc9f78\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 2) and (3, 1).\" \/>\r\n\r\nc) [latex]y=-7x+3[\/latex]\r\n\r\nd) [latex]y = -2[\/latex]\r\n\r\n[reveal-answer q=\"776287\"]Show Solutions[\/reveal-answer]\r\n[hidden-answer a=\"776287\"]\r\n\r\n(a) The slope is positive\r\n\r\nb) The slope is negative\r\n\r\nc) [latex]y=-7x+3[\/latex]. The coefficient of [latex]x[\/latex] is [latex]-7[\/latex]. Since [latex]-7[\/latex] is negative, the slope is negative.\r\n\r\nd) [latex]y = -2[\/latex]. Since there is no [latex]x[\/latex] term, the coefficient of [latex]x[\/latex] is [latex]0[\/latex]. The slope is zero.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/section>\r\n<div class=\"h-8\"><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]310296[\/ohm_question]<\/section><\/div>\r\n<section aria-label=\"Try It\"><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]310297[\/ohm_question]<\/section><\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Recognize positive, negative, and zero slope<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\n<h3>sign of slope<\/h3>\n<p class=\"whitespace-normal break-words\">The sign of a slope tells us the direction a line moves:<\/p>\n<ul class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-disc space-y-1.5 pl-7\">\n<li class=\"whitespace-normal break-words\">Positive slope: Line rises from left to right<\/li>\n<li class=\"whitespace-normal break-words\">Negative slope: Line falls from left to right<\/li>\n<li class=\"whitespace-normal break-words\">Zero slope: Line is horizontal<\/li>\n<li class=\"whitespace-normal break-words\">Undefined slope: Line is vertical<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/openstax.org\/apps\/image-cdn\/v1\/f=webp\/apps\/archive\/20250522.165258\/resources\/40350686e52f6175268fa33a48576e28e387a022\" alt=\"The image shows four arrows. The first arrow is slanted and pointing up and to the right and is labeled \u201cpositive\u201d. The second arrow is slanted and pointing down and to the right and labeled \u201cnegative\u201d. The third arrow is horizontal and labeled \u201czero\u201d. The fourth arrow is vertical and labeled \u201cundefined\u201d.\" \/><\/p>\n<\/section>\n<section class=\"textbox recall\" aria-label=\"Recall\">For lines given in the form [latex]y=mx+b[\/latex], slope is [latex]m[\/latex], the coefficient of [latex]x[\/latex].<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">Identify the type of slope for each scenario:a)<img decoding=\"async\" src=\"https:\/\/openstax.org\/apps\/image-cdn\/v1\/f=webp\/apps\/archive\/20250522.165258\/resources\/d17d908fe193fcd7fdb1e0872ae05773588f142f\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, negative 2) and (3, 3).\" \/>b)<img decoding=\"async\" src=\"https:\/\/openstax.org\/apps\/image-cdn\/v1\/f=webp\/apps\/archive\/20250522.165258\/resources\/fff70f8e7e94cf3dfa4eb66a0cc94a2abbdc9f78\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 2) and (3, 1).\" \/><\/p>\n<p>c) [latex]y=-7x+3[\/latex]<\/p>\n<p>d) [latex]y = -2[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q776287\">Show Solutions<\/button><\/p>\n<div id=\"q776287\" class=\"hidden-answer\" style=\"display: none\">\n<p>(a) The slope is positive<\/p>\n<p>b) The slope is negative<\/p>\n<p>c) [latex]y=-7x+3[\/latex]. The coefficient of [latex]x[\/latex] is [latex]-7[\/latex]. Since [latex]-7[\/latex] is negative, the slope is negative.<\/p>\n<p>d) [latex]y = -2[\/latex]. Since there is no [latex]x[\/latex] term, the coefficient of [latex]x[\/latex] is [latex]0[\/latex]. The slope is zero.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<div class=\"h-8\">\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm310296\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=310296&theme=lumen&iframe_resize_id=ohm310296&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<section aria-label=\"Try It\">\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm310297\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=310297&theme=lumen&iframe_resize_id=ohm310297&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n","protected":false},"author":13,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":36,"module-header":"- Select Header -","content_attributions":[],"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\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/471"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/13"}],"version-history":[{"count":8,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/471\/revisions"}],"predecessor-version":[{"id":5143,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/471\/revisions\/5143"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/36"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/471\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=471"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=471"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=471"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}