{"id":11214,"date":"2017-05-09T14:34:19","date_gmt":"2017-05-09T06:34:19","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=11214"},"modified":"2017-05-09T15:39:47","modified_gmt":"2017-05-09T07:39:47","slug":"new-applet-domain-range-investigation","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/new-applet-domain-range-investigation-11214","title":{"rendered":"New applet: Domain and range investigation"},"content":{"rendered":"<p>I recently added a <a href=\"https:\/\/www.intmath.com\/functions-and-graphs\/domain-range-interactive.php\">new interactive applet<\/a> that helps you explore the concepts of domain and range. This accompanies one of the most popular pages on IntMath, <a href=\"https:\/\/www.intmath.com\/functions-and-graphs\/2a-domain-and-range.php\">Domain and Range of a Function<\/a>. <\/p>\n<p>Most students don't have much trouble with finding the <strong>domain<\/strong> of a function (by avoiding negative values under a square root, or zero values in the denominator of a fraction), but figuring out the resulting <strong>range<\/strong> can be a challenge.<\/p>\n<p>Many of us are  visual learners and it's certainly true that if you have a reasonable idea of what a function looks like in general, then determining the domain and range is a lot easier.<\/p>\n<p>For some examples of what I mean,<\/p>\n<ul>\n<li>A <strong>linear function<\/strong> (like <span class=\"intmath\"><em>y<\/em> = 3<em>x<\/em> + 2<\/span>) has no restrictions on the <em>x<\/em>-values, and  all <em>y<\/em>-values will result    <\/li>\n<li>A <strong>quadratic function <\/strong>(like <span class=\"intmath\"><em>y<\/em> = 2<em>x<\/em><sup>2<\/sup> &minus; 5<\/span>) has no restrictions on the <em>x<\/em>-values (the domain), but only half of the possible <em>y<\/em>-values (the range) on the plane will be output<\/li>\n<li>A <strong>sine function <\/strong>(like <span class=\"intmath\"><em>y<\/em> = 4 sin <em>x<\/em><\/span>) has no restrictions on the <em>x<\/em>-values, and  all the resulting <em>y<\/em>-values will be between <span class=\"intmath\">4<\/span> and <span class=\"intmath\">&minus;4.<\/span><\/li>\n<li>A <strong>hyperbola<\/strong> (like <span class=\"intmath\"><em>y<\/em> = 3\/<em>x<\/em><\/span>) is not defined for <span class=\"intmath\"><em>x<\/em> = 0<\/span>, and   the resulting <em>y<\/em>-values will be all values except  <span class=\"intmath\">0.<\/span><\/li>\n<\/ul>\n<p>How do I know these? It's from having a good idea of what each function looks like in general. I then just need to look at the specific numbers involved and can determine the domain and range without drawing a graph. But how do you learn the general shapes? <\/p>\n<h2>The new applet<\/h2>\n<p>The new <a href=\"https:\/\/www.intmath.com\/functions-and-graphs\/domain-range-interactive.php\">interactive domain and range interactive applet<\/a> allows you to explore several different functions and see what effect a change in domain makes to the range.<\/p>\n<p>Here are some screen shots:<\/p>\n<div class=\"imgCenter\">\n  <a href=\"https:\/\/www.intmath.com\/functions-and-graphs\/domain-range-interactive.php\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2017\/05\/domain-range-sinx.png\" alt=\"domain and range - sine curve\" width=\"297\" height=\"299\" \/><\/a>  <br \/>\n  Domain and range of a sine curve <\/div>\n<p>This next one has a restriction on the domain:<\/p>\n<div class=\"imgCenter\">\n  <a href=\"https:\/\/www.intmath.com\/functions-and-graphs\/domain-range-interactive.php\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2017\/05\/domain-range-parabola.png\" alt=\"domain and range - restricted parabola\" width=\"297\" height=\"299\" \/><\/a>  <br \/>\n  Domain and range of a parabola with restricted domain <\/div>\n<p>There are also ones with discontinuities:<\/p>\n<div class=\"imgCenter\">\n  <a href=\"https:\/\/www.intmath.com\/functions-and-graphs\/domain-range-interactive.php\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2017\/05\/domain-range-1onxplus2.png\" alt=\"domain and range - hyperbola\" width=\"297\" height=\"299\" \/><\/a>  <br \/>\n  Hyperbola domain and range <\/div>\n<h2>Technical bit<\/h2>\n<p>To produce the graphs, I'm using AsciiSVG-IM.js, which creates an SVG (scalar vector graphics) image. Here's some background and a demo: <a href=\"https:\/\/www.intmath.com\/cg3\/asciisvg-im-js-demo.php\">AsciiSVG-IM.js Syntax and Demo<\/a>. I also used this small library for the <a href=\"https:\/\/www.intmath.com\/functions-and-graphs\/graphs-using-svg.php\">Online Graphing Calculator<\/a> and <a href=\"https:\/\/www.intmath.com\/methods-integration\/riemann-sums-negatives-discontinuities.php\">Riemann Sums - Negative Integrals and Discontinuities<a\/>.<\/p>\n<p>Let me know what you think in the comments below. <\/p>\n<p class=\"alt\"><a href=\"#respond\" id=\"comms\">Be the first to comment<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p> <a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/new-applet-domain-range-investigation-11214\"><img loading=\"lazy\" src=\"https:\/\/www.intmath.com\/blog\/wp-content\/images\/2017\/05\/domain-range_th.png\" alt=\"domain and range applet\" width=\"128\" height=\"100\" class=\"imgRt\" \/><\/a><br \/>This interactive applet allows you to explore the concepts of domain and range for several different mathematical functions.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[4],"tags":[134,109],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/11214"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=11214"}],"version-history":[{"count":6,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/11214\/revisions"}],"predecessor-version":[{"id":11220,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/11214\/revisions\/11220"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=11214"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=11214"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=11214"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}