{"id":5337,"date":"2022-02-06T17:53:41","date_gmt":"2022-02-06T17:53:41","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=5337"},"modified":"2022-02-06T17:53:41","modified_gmt":"2022-02-06T17:53:41","slug":"comparing-functions","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/comparing-functions\/","title":{"rendered":"Comparing Functions"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″ css=”.vc_custom_1633761494145{border-radius: 1px !important;}”][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Comparing Functions<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]A function in math is visualized as a rule, which gives a unique output for every input x. There are many ways to represent functions. For example, a function can be represented with an input-output table , with a graph, and with an equation.<\/p>\n<p>Sometimes a problem asks us to compare two functions which are represented in different ways. For example, you might be given a table and a graph, and asked which function is greater for a particular value, or which function increases faster.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]Compare two functions by determining the rate of change.<\/p>\n<p><strong>To find the rate of change from a linear function:<\/strong><br \/>\nThe coefficient of x (slope) is the rate of change of the linear function.<\/p>\n<p><strong>To find the rate of change from a linear function graph:<\/strong><br \/>\n1. Select any two ordered pairs from the graph.<br \/>\n2. Subtract the y-coordinates of both ordered pairs to find the vertical change. This is the rise.<br \/>\n3. Subtract the x-coordinates of both ordered pairs to find the horizontal change. This is the run.<br \/>\n4. Calculate the slope by dividing the rise by the run.<\/p>\n<p><strong>To find the rate of change from a function table:<\/strong><br \/>\n1. Select any two ordered pairs from the table.<br \/>\n2. Subtract the y-coordinates of both ordered pairs to find the vertical change. This is the rise.<br \/>\n3. Subtract the x-coordinates of both ordered pairs to find the horizontal change. This is the run.<br \/>\n4. Calculate the slope by dividing the rise by the run. [\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">The number of sales (y) per day (x) on Jane’s website can be represented by y = 12x.<br \/>\nThe number of sales on Sarah’s website is shown in the graph below. Whose website gets more sales per day?<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/compare-properties-of-functions\"><img loading=\"lazy\" class=\"alignnone wp-image-5339 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/8-20.png\" alt=\"\" width=\"297\" height=\"323\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/8-20.png 297w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/8-20-276x300.png 276w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/a><\/span><\/strong><br \/>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]The rate of Jane’s sales is 12 sales\/day. The graph of Sarah’s sales has a rate of change of <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\frac{10}{1}\" alt=\"\\fn_phv \\frac{10}{1}\" align=\"absmiddle\" \/>, so she gets 10 sales\/day.<\/p>\n<p><span style=\"color: red;\"><strong>Jane’s website gets more sales per day.<\/strong><\/span>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Comparing Functions[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">You have recently begun searching for phone billing plans. Phone Company A charges can be represented by the equation y = 0.2x, where x represents the number of texts you send a month and y is the total bill for the month. The billing plan for phone company B is represented by the table below. Which company has the lowest rate for texts?<\/span><\/strong><br \/>\nRound your answers to the nearest hundredths.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/compare-properties-of-functions\"><img loading=\"lazy\" class=\"alignnone wp-image-5341 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/9-18.png\" alt=\"\" width=\"300\" height=\"223\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/compare-properties-of-functions”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">Nick and Alyssa are racing up a wall. Alyssa’s height on the wall is given by the equation a = <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\dpi{100}&space;\\fn_phv&space;{\\color{Teal}&space;\\frac{1}{3}}\" alt=\"\\dpi{100} \\fn_phv {\\color{Teal} \\frac{1}{3}}\" align=\"absmiddle\" \/>t + 5, where (a) is Alyssa’s height in meters after climbing (t) minutes. Nick started racing at the same time as Alyssa and is also climbing at a constant speed. His height is shown in the table below. Who is climbing at a slower rate?<\/span><\/strong><br \/>\nRound your answers to the nearest tenths.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/compare-properties-of-functions\"><img loading=\"lazy\" class=\"alignnone wp-image-5343 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/10-13.png\" alt=\"\" width=\"295\" height=\"167\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/compare-properties-of-functions”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">The amount of money saved (y) after a number of days (x) for Adam is represented by the graph below. The amount of money saved (y) after a number of days (x) for Bianca is represented by the table. Who is saving more money per day?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/compare-properties-of-functions\"><img loading=\"lazy\" class=\"alignnone wp-image-5345 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/11-13.png\" alt=\"\" width=\"294\" height=\"535\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/11-13.png 294w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/11-13-165x300.png 165w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/compare-properties-of-functions”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Function<\/strong> – is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).<\/p>\n<p><strong>Rate of Change<\/strong> – ratio of the “vertical change” to the “horizontal change” between (any) two distinct points on a line. It is also called the slope.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/slope\"><span style=\"color: #ed5600;\">Slope<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/representing-relationships\"><span style=\"color: #ed5600;\">Representing Relationships<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/relations\"><span style=\"color: #ed5600;\">Relations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/functions\"><span style=\"color: #ed5600;\">Functions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/linear-functions\"><span style=\"color: #ed5600;\">Linear Functions<\/span><\/a><br \/>\n[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1637241856065{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/construct-functions\"><span style=\"color: #333399;\">Construct Functions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/linear-and-nonlinear-functions\"><span style=\"color: #333399;\">Linear and Nonlinear Functions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/quadratic-functions\"><span style=\"color: #333399;\">Quadratic Functions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/qualitative-graphs\"><span style=\"color: #333399;\">Qualitative Graphs<\/span><\/a><br \/>\n[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||”][vc_btn title=”Grade 5″ color=”green” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||”][vc_btn title=”Grade 6″ color=”info” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F6th-grade%2Fmaths|title:Grade%206%20Math||”][vc_btn title=”Grade 7″ color=”vista-blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F7th-grade%2Fmaths|title:Grade%207%20Math||”][vc_btn title=”Grade 8″ color=”mulled-wine” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F8th-grade%2Fmaths|title:Grade%208%20Math||”][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Functions and equations” color=”warning” link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Ffunctions-and-equations|title:Functions%20and%20equations||”][vc_btn title=”Graphs” color=”danger” link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Fgraphs|title:Graphs||”][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″ css=”.vc_custom_1633761494145{border-radius: 1px !important;}”][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Comparing Functions [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]A function in math is visualized as a rule, which gives a unique output for every input x. There are many ways to represent functions. For […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Comparing Functions | Oryx Learning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/comparing-functions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Comparing Functions\" \/>\n<meta property=\"og:description\" content=\"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″ css=”.vc_custom_1633761494145{border-radius: 1px !important;}”][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Comparing Functions [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]A function in math is visualized as a rule, which gives a unique output for every input x. There are many ways to represent functions. For […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/oryxlearning.com\/learn\/comparing-functions\/\" \/>\n<meta property=\"og:site_name\" content=\"Oryx Learning\" \/>\n<meta property=\"og:image\" content=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/8-20.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/#organization\",\"name\":\"Oryx Learning\",\"url\":\"https:\/\/oryxlearning.com\/learn\/\",\"sameAs\":[],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/Oryx-Learning-Logo-3.png\",\"contentUrl\":\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/Oryx-Learning-Logo-3.png\",\"width\":150,\"height\":74,\"caption\":\"Oryx Learning\"},\"image\":{\"@id\":\"https:\/\/oryxlearning.com\/learn\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/#website\",\"url\":\"https:\/\/oryxlearning.com\/learn\/\",\"name\":\"Oryx Learning\",\"description\":\"Complete interactive math curriculum\",\"publisher\":{\"@id\":\"https:\/\/oryxlearning.com\/learn\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/oryxlearning.com\/learn\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/comparing-functions\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/8-20.png\",\"contentUrl\":\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/8-20.png\",\"width\":297,\"height\":323},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/comparing-functions\/#webpage\",\"url\":\"https:\/\/oryxlearning.com\/learn\/comparing-functions\/\",\"name\":\"Comparing Functions | Oryx Learning\",\"isPartOf\":{\"@id\":\"https:\/\/oryxlearning.com\/learn\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/oryxlearning.com\/learn\/comparing-functions\/#primaryimage\"},\"datePublished\":\"2022-02-06T17:53:41+00:00\",\"dateModified\":\"2022-02-06T17:53:41+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/oryxlearning.com\/learn\/comparing-functions\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/oryxlearning.com\/learn\/comparing-functions\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/comparing-functions\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/oryxlearning.com\/learn\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Comparing Functions\"}]}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Comparing Functions | Oryx Learning","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/oryxlearning.com\/learn\/comparing-functions\/","og_locale":"en_US","og_type":"article","og_title":"Comparing Functions","og_description":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″ css=”.vc_custom_1633761494145{border-radius: 1px !important;}”][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Comparing Functions [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]A function in math is visualized as a rule, which gives a unique output for every input x. There are many ways to represent functions. 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