{"id":4324,"date":"2013-06-29T03:58:42","date_gmt":"2013-06-29T03:58:42","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=4324"},"modified":"2026-03-25T11:04:40","modified_gmt":"2026-03-25T16:04:40","slug":"domain-and-range","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/domain-and-range\/","title":{"rendered":"How to Find Domain and Range"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_QFPFmi48ZdM\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_QFPFmi48ZdM\" data-source-videoID=\"QFPFmi48ZdM\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"How to Find Domain and Range Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"How to Find Domain and Range\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_QFPFmi48ZdM:hover {cursor:pointer;} img#videoThumbnailImage_QFPFmi48ZdM {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/07\/updated-how-to-find-domain-and-range-64bfeac37bc89-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_QFPFmi48ZdM\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_QFPFmi48ZdM\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"How to Find Domain and Range\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_QFPFmi48ZdM\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_QFPFmi48ZdM\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_QFPFmi48ZdM\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction aVn_Function() {\n  var x = document.getElementById(\"aVn\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"aVn_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"aVn\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_Domain\" class=\"smooth-scroll\">What is Domain?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#What_is_Range\" class=\"smooth-scroll\">What is Range?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Linear_Functions\" class=\"smooth-scroll\">Linear Functions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Domain_and_Range_Practice_Questions\" class=\"smooth-scroll\">Domain and Range Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello, and welcome to this video on domain and range! In this video, we will see:<\/p>\n<ul>\n<li>What domain and range are<\/li>\n<li>And how to find the domain and range of a function<\/li>\n<\/ul>\n<p>Remember, a <strong>function<\/strong> is a relation between two sets of numbers, an input and an output. Each element of the input produces a unique element of the output. <\/p>\n<h2><span id=\"What_is_Domain\" class=\"m-toc-anchor\"><\/span>What is Domain?<\/h2>\n<p>\nThe <strong>domain<\/strong> of a function is the set of all possible inputs of a function. This means it is any number you can plug into a function. For most functions, this will be any number you can plug in for the letter \\(x\\). Almost every time, your domain will be all real numbers, except for a few special cases like <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/roots\/\">square root<\/a> functions and rational numbers.<\/p>\n<h2><span id=\"What_is_Range\" class=\"m-toc-anchor\"><\/span>What is Range?<\/h2>\n<p>\nThe <strong>range<\/strong> of a function is the set of all of the possible outputs of a function. Typically, this will be represented by the letter \\(y\\) or \\(f(x)\\). The range is any number that you can get when you plug in any number for \\(x\\).<\/p>\n<h2><span id=\"Linear_Functions\" class=\"m-toc-anchor\"><\/span>Linear Functions<\/h2>\n<p>\nLet\u2019s look at a simple linear function: \\(y = 4x + 3\\). We are going to find the domain and range using just the equation, by looking at a graph, and by looking at a table.<\/p>\n<p>Let\u2019s think about this algebraically for a minute. The domain is any number we can put in place of the \\(x\\). You could put 1, 2, -7, 84, or any other number in place of the \\(x\\). This means that the domain is: \\(-\\infty\\leq x\\leq\\infty\\). Another way to say this is that the domain is the set of all real numbers.<\/p>\n<p>What about our range? Well, if I plug in 1 for \\(x\\), I get 7 and if I plug in 2 for \\(x\\), I get 11. But I can also plug in 1.5 for \\(x\\), which would give me 9, or 1.25 for \\(x\\), which would give me 8. I can plug in any decimal number, so for this equation, I can also get out any number for \\(y\\) by searching for the right \\(x\\). <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-65195\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/possible-replacements-for-x-280x300.png\" alt=\"replacements for x\" width=\"280\" height=\"300\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/possible-replacements-for-x-280x300.png 280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/possible-replacements-for-x-768x821.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/possible-replacements-for-x.png 848w\" sizes=\"auto, (max-width: 280px) 100vw, 280px\" \/><\/p>\n<p>The range of this function is also the set of all real numbers.<\/p>\n<p>Now I want to check this graphically. If we graph this function, we see that it is a line. Lines continue across every value of \\(x\\) and every value of \\(y\\). This matches up with what we found out by thinking through it algebraically. This further proves that domain and range are both the set of all real numbers.<\/p>\n<p>Now let\u2019s look at a table of values for the first four terms of this function.<\/p>\n<table class=\"ATable\" style=\"margin: auto;\">\n<thead>\n<tr>\n<th>\\(x\\)<\/th>\n<th>\\(y\\)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1<\/td>\n<td>7<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>11<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>15<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>19<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\n&nbsp;<br \/>\nIn this case, we are only looking at a portion of the function, so our domain of values would be {1, 2, 3, and 4} and our range of values would be {7, 11, 15, and 19}.<br \/>\nLet\u2019s try a couple of examples. What is the domain and range of the function \\(y=x^{2}-4x+3\\)?<\/p>\n<p>The domain is the list of numbers that can be plugged in for \\(x\\). You can plug in any number for \\(x\\), so the domain is the set of all real numbers.<\/p>\n<p>What about our range? Let\u2019s figure this out by looking at a graph of the equation. <\/p>\n<p>Remember, our range is every possible value for \\(y\\). If we look at our graph, we see that it is a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/parabolas\/\">parabola<\/a> that opens up with a vertex at \\((2, -7)\\). <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-65194\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/graph-1-1-300x290.png\" alt=\"parabola\" width=\"300\" height=\"290\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/graph-1-1-300x290.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/graph-1-1-768x742.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/graph-1-1.png 937w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>This means that our range is \\(y\\geq-7\\).<\/p>\n<p>Let\u2019s try one more example, this time using a table for the function \\(y=2x\u20131\\).<\/p>\n<table class=\"ATable\" style=\"margin: auto;\">\n<thead>\n<tr>\n<th>\\(x\\)<\/th>\n<th>\\(y\\)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>7<\/td>\n<td>13<\/td>\n<\/tr>\n<tr>\n<td>14<\/td>\n<td>27<\/td>\n<\/tr>\n<tr>\n<td>21<\/td>\n<td>41<\/td>\n<\/tr>\n<tr>\n<td>28<\/td>\n<td>55<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\n&nbsp;<br \/>\nWhat would be our domain and range given this table? Our domain would be {7, 14, 21, and 28} and our range would be {13, 27, 41, and 55}.<\/p>\n<p>If we wanted the domain and range for the whole function, we would consider what numbers we can plug in for \\(x\\) and what corresponding \\(y\\)-values we would get. Well, we can plug in any number for \\(x\\), and it is a linear function, so we can get any number for \\(y\\). Therefore, the domain and range of this function is all real numbers.<\/p>\n<p>Remember, if you are finding the domain and range of a function algebraically, think about what numbers you can plug in for \\(x\\) and the resulting numbers you will get for \\(y\\). If you are finding the domain and range given a graph, follow your finger along the graph and see what \\(x\\)-values it covers and what \\(y\\)-values it covers. <\/p>\n<p>Finally, if you are looking at a table, the domain is the list of numbers inputted for \\(x\\) and the range is the list of numbers that are the outputs of those \\(x\\) inputs, the numbers in the \\(y\\) column.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-65192\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/domain-and-range-1024x465.png\" alt=\"finding domain and range\" width=\"1024\" height=\"465\" style=\"box-shadow: 1.5px 1.5px  3px gray;\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/domain-and-range-1024x465.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/domain-and-range-300x136.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/domain-and-range-768x349.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/domain-and-range-1536x697.png 1536w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/domain-and-range.png 1892w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>I hope this video on domain and range was helpful! Thanks for watching and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Domain_and_Range_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Domain and Range Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe linear equation \\(y=2x+3\\) is graphed below. Use the graph to determine the domain and range. Remember that the red line continues off the graph indefinitely in both directions.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Domain-and-range-graph-1.svg\" alt=\"A red straight line with positive slope crosses the y-axis above the origin and the x-axis to the left of the origin on a Cartesian grid.\" width=\"294.4\" height=\"322\" class=\"aligncenter size-full wp-image-274153\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\"><span style=\"font-weight: 600\">Domain:<\/span> numbers less than 10<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> all real numbers<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\"><span style=\"font-weight: 600\">Domain:<\/span> all real numbers<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> all real numbers<\/div><div class=\"PQ\"  id=\"PQ-1-3\"><span style=\"font-weight: 600\">Domain:<\/span> values greater than 10<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> all real numbers<\/div><div class=\"PQ\"  id=\"PQ-1-4\"><span style=\"font-weight: 600\">Domain:<\/span> no solutions<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> all real numbers<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The domain refers to all possible inputs that you can plug into the function. In this case, the red line on the graph shows that any value can be plugged in for \\(x\\). Therefore, the domain is all real numbers.<\/p>\n<p>To find the range, look for all possible outputs of the function, or all values for \\(y\\) that appear on the graph. The graphed red line reveals that any value for \\(y\\) is possible, which means the domain is also all real numbers.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe quadratic function \\(y=x^2+4x+3\\) is graphed below. Use the graph to determine the domain and range.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Domain-and-range-graph-2.svg\" alt=\"A red parabola opens upward on a grid, with its vertex near (-2, -1) and crossing the y-axis at 3 and the x-axis between -3 and -1.\" width=\"607.2\" height=\"472.65\" class=\"aligncenter size-full wp-image-274156\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\"><span style=\"font-weight: 600\">Domain:<\/span> \\(x \\geq -1\\)<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> no solutions<\/div><div class=\"PQ\"  id=\"PQ-2-2\"><span style=\"font-weight: 600\">Domain:<\/span> \\(x \\geq 3\\)<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> all real numbers<\/div><div class=\"PQ\"  id=\"PQ-2-3\"><span style=\"font-weight: 600\">Domain:<\/span> no solution<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> \\(y \\geq -3\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-4\"><span style=\"font-weight: 600\">Domain:<\/span> all real numbers<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> \\(y \\geq -1\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The graph shows that all values of \\(x\\) are represented somewhere on the red line, because the line reaches out to the left and right and doesn&#8217;t end. This means the domain is all real numbers.<\/p>\n<p>However, when looking at the range, notice that the red line stops at \u22121 for \\(y\\) values. This means that values for \\(y\\) are only at or above \u22121, which is represented by \\(y \\geq -1\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe table below represents only the first four terms of a function. This is only a small portion of the data that could be represented from the graph of \\(y=-2x+7\\). Which values represent range?<\/p>\n<table class=\"ATable\" style=\"margin: auto; width: 50%\">\n<thead>\n<tr>\n<th><strong>A<\/strong><\/th>\n<th><strong>B<\/strong><\/th>\n<\/tr>\n<tbody>\n<tr>\n<td>1<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>-1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">Column A<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">Column B<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>This can be determined by plugging in a value on the left into the equation. The result is the value on the right. Every value on the left is an input, and every value on the right is an output.<\/p>\n<p>For example, if we plug in 1 for \\(x\\), we get 5 as the output for \\(y\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nFind the domain and range for the following linear equation:<\/p>\n<div class=\"yellow-math-quote\">\\(y=5x+7\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\"><span style=\"font-weight: 600\">Domain:<\/span> all real numbers<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> all real numbers<\/div><div class=\"PQ\"  id=\"PQ-4-2\"><span style=\"font-weight: 600\">Domain:<\/span> all real numbers<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> \\(y \\geq 7\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\"><span style=\"font-weight: 600\">Domain:<\/span> \\(x \\geq 5\\)<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> \\(y \\gt 5\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\"><span style=\"font-weight: 600\">Domain:<\/span> no real solutions<br>\r\n<span style=\"font-weight: 600\">Range:<\/span> all real numbers<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The domain and range for this linear equation can be determined algebraically. There is nothing that prevents plugging in any value for \\(x\\), so the domain is all real numbers. The \\(y\\)-values, or outputs, are simply a reflection of what is input.<\/p>\n<p>Since any value can be plugged in for and this is a linear equation, the values for \\(y\\) are also unlimited. The values for \\(x\\) are unlimited as well as the values for \\(y\\), so the range is also all real numbers.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich table shows the correct domain and range for the linear equation \\(y=2x+3\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\"><table class=\"ATable\" style=\"width: 30%\">\r\n<thead>\r\n<tr>\r\n<th><strong>\\(x\\)<\/strong><\/th>\r\n<th><strong>\\(f(x)\\)<\/strong><\/th>\r\n<\/tr>\r\n<tbody>\r\n<tr>\r\n<td style=\"background-color: white\">1<\/td>\r\n<td style=\"background-color: white\">2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">2<\/td>\r\n<td style=\"background-color: white\">4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">3<\/td>\r\n<td style=\"background-color: white\">6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">4<\/td>\r\n<td style=\"background-color: white\">8<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table><\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\"><table class=\"ATable\" style=\"width: 30%\">\r\n<thead>\r\n<tr>\r\n<th><strong>\\(x\\)<\/strong><\/th>\r\n<th><strong>\\(f(x)\\)<\/strong><\/th>\r\n<\/tr>\r\n<tbody>\r\n<tr>\r\n<td style=\"background-color: white\">1<\/td>\r\n<td style=\"background-color: white\">5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">2<\/td>\r\n<td style=\"background-color: white\">7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">3<\/td>\r\n<td style=\"background-color: white\">9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">4<\/td>\r\n<td style=\"background-color: white\">11<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table><\/div><div class=\"PQ\"  id=\"PQ-5-3\"><table class=\"ATable\" style=\"width: 30%\">\r\n<thead>\r\n<tr>\r\n<th><strong>\\(x\\)<\/strong><\/th>\r\n<th><strong>\\(f(x)\\)<\/strong><\/th>\r\n<\/tr>\r\n<tbody>\r\n<tr>\r\n<td style=\"background-color: white\">1<\/td>\r\n<td style=\"background-color: white\">4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">2<\/td>\r\n<td style=\"background-color: white\">3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">3<\/td>\r\n<td style=\"background-color: white\">2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">4<\/td>\r\n<td style=\"background-color: white\">1<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table><\/div><div class=\"PQ\"  id=\"PQ-5-4\"><table class=\"ATable\" style=\"width: 30%\">\r\n<thead>\r\n<tr>\r\n<th><strong>\\(x\\)<\/strong><\/th>\r\n<th><strong>\\(f(x)\\)<\/strong><\/th>\r\n<\/tr>\r\n<tbody>\r\n<tr>\r\n<td style=\"background-color: white\">1<\/td>\r\n<td style=\"background-color: white\">5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">2<\/td>\r\n<td style=\"background-color: white\">9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">3<\/td>\r\n<td style=\"background-color: white\">11<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"background-color: white\">4<\/td>\r\n<td style=\"background-color: white\">8<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Input values are represented by \\(x\\), and \\(f(x)\\) represents the output values, or \\(y\\).<\/p>\n<p>Table B can be tested algebraically to make sure that each input value results in the appropriate output value. If 1 is plugged in for \\(x\\), the result is 5. If 2 is plugged in for \\(x\\), the result is 7.<\/p>\n<p>Table B shows input and output values that match with the given equation.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-ii\/\">Return to Algebra II Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Algebra II Videos<\/p>\n","protected":false},"author":1,"featured_media":99712,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-4324","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-domain-and-range-videos","7":"page_category-math-advertising-group","8":"page_category-video-pages-for-study-course-sidebar-ad","9":"page_type-video","10":"content_type-practice-questions","11":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4324","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=4324"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4324\/revisions"}],"predecessor-version":[{"id":279118,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4324\/revisions\/279118"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/99712"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=4324"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}