{"id":27713,"date":"2025-06-20T06:06:06","date_gmt":"2025-06-20T06:06:06","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=27713"},"modified":"2025-06-20T06:06:07","modified_gmt":"2025-06-20T06:06:07","slug":"identify-where-the-function-is-increasing-on-the-intervals-decreasing-on-the-intervals","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/identify-where-the-function-is-increasing-on-the-intervals-decreasing-on-the-intervals\/","title":{"rendered":"Identify where the function is: Increasing on the interval(s) Decreasing on the interval(s)"},"content":{"rendered":"\n<p>Use inequality notation<br>or<br>etc. to identify where the function is: Increasing on the interval(s) Decreasing on the interval(s)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"566\" height=\"381\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-79.png\" alt=\"\" class=\"wp-image-27714\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-79.png 566w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-79-300x202.png 300w\" sizes=\"auto, (max-width: 566px) 100vw, 566px\" \/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Increasing on the interval(s):<\/strong> \u22124&lt;x&lt;\u22122-4 &lt; x &lt; -2\u22124&lt;x&lt;\u22122 and 0&lt;x&lt;20 &lt; x &lt; 20&lt;x&lt;2<\/li>\n\n\n\n<li><strong>Decreasing on the interval(s):<\/strong> \u2212\u221e&lt;x\u2264\u22124-\\infty &lt; x \\le -4\u2212\u221e&lt;x\u2264\u22124, \u22122\u2264x\u22640-2 \\le x \\le 0\u22122\u2264x\u22640, and 2\u2264x&lt;\u221e2 \\le x &lt; \\infty2\u2264x&lt;\u221e<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation (without using em dashes):<\/strong><\/p>\n\n\n\n<p>To determine where the function is increasing or decreasing, we analyze the graph by looking at how the function behaves as we move from left to right along the x-axis.<\/p>\n\n\n\n<p>A function is <strong>increasing<\/strong> on an interval if the y-values (output) rise as the x-values (input) move from left to right. In contrast, a function is <strong>decreasing<\/strong> on an interval if the y-values drop as the x-values increase.<\/p>\n\n\n\n<p>From the graph:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>From the far left to x = -4<\/strong>, the graph is going downwards. This means the function is decreasing on the interval where x\u2264\u22124x \\le -4x\u2264\u22124.<\/li>\n\n\n\n<li><strong>From x = -4 to x = -2<\/strong>, the graph rises. This indicates the function is increasing on the interval \u22124&lt;x&lt;\u22122-4 &lt; x &lt; -2\u22124&lt;x&lt;\u22122.<\/li>\n\n\n\n<li><strong>From x = -2 to x = 0<\/strong>, the graph descends again. The function is decreasing on the interval \u22122\u2264x\u22640-2 \\le x \\le 0\u22122\u2264x\u22640.<\/li>\n\n\n\n<li><strong>From x = 0 to x = 2<\/strong>, the graph goes up. This part of the graph shows the function is increasing on the interval 0&lt;x&lt;20 &lt; x &lt; 20&lt;x&lt;2.<\/li>\n\n\n\n<li><strong>From x = 2 onward<\/strong>, the graph drops steeply, so the function is decreasing for x\u22652x \\ge 2x\u22652.<\/li>\n<\/ol>\n\n\n\n<p>We express these intervals using inequality notation. We use strict inequalities &lt;&lt;&lt; when the function is clearly increasing or decreasing between two points. We use \u2264\\le\u2264 at the turning points to show that the function changes direction exactly at those points.<\/p>\n\n\n\n<p>Understanding these patterns helps analyze many types of functions. This skill is especially important in calculus and other areas of math that study rates of change.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-171.jpeg\" alt=\"\" class=\"wp-image-27715\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-171.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-171-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-171-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Use inequality notationoretc. to identify where the function is: Increasing on the interval(s) Decreasing on the interval(s) The Correct Answer and Explanation is: Correct Answer: Explanation (without using em dashes): To determine where the function is increasing or decreasing, we analyze the graph by looking at how the function behaves as we move from left [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-27713","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27713","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=27713"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27713\/revisions"}],"predecessor-version":[{"id":27716,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27713\/revisions\/27716"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=27713"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=27713"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=27713"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}