{"id":18,"date":"2013-03-31T01:15:34","date_gmt":"2013-03-31T00:15:34","guid":{"rendered":"http:\/\/www.lovemaths.fr\/blog_en\/?p=18"},"modified":"2013-03-31T01:17:03","modified_gmt":"2013-03-31T00:17:03","slug":"y-3%e2%88%9a16-x22x17-and-y-3%e2%88%9a16-x22x17-whats-this","status":"publish","type":"post","link":"https:\/\/www.lovemaths.fr\/blog_en\/?p=18","title":{"rendered":"y = 3\u221a[(16-x^2)\/(2x+17)] and y = -3\u221a[(16-x^2)\/(2x+17)] what\u2019s this ?"},"content":{"rendered":"<p style=\"text-align: justify;\"><a href=\"http:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-19 alignleft\" alt=\"func\" src=\"http:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func2.png\" width=\"274\" height=\"57\" \/><\/a><br \/>\nwhat is this?<\/p>\n<p style=\"text-align: justify;\">\u00a0.<\/p>\n<p style=\"text-align: justify;\">What a funny question! We can first do a study of the two associated functions.<\/p>\n<p style=\"text-align: justify;\">\u00a0<a href=\"http:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-20 alignleft\" alt=\"func\" src=\"http:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func3-300x147.png\" width=\"300\" height=\"147\" srcset=\"https:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func3-300x147.png 300w, https:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func3.png 333w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>We are told that the domain of definition of both functions is ]-\u221e ;-17\/2[ U [-4\u00a0;4] and that the tables of variations are those on the left side (we can see here the differences, translated into \u201csymmetries\u201d, due to the minus sign).<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">But we still do not have a clear explanation! Let\u2019s have a look at each curve.<\/p>\n<p style=\"text-align: justify;\"><a href=\"http:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func4.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-21 alignleft\" alt=\"func\" src=\"http:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func4-226x300.png\" width=\"226\" height=\"300\" srcset=\"https:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func4-226x300.png 226w, https:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func4.png 254w\" sizes=\"auto, (max-width: 226px) 100vw, 226px\" \/><\/a><\/p>\n<p style=\"text-align: justify;\">They are both conforming to the previous tables of variations. It is possible to notice the horizontal tangents (and the symmetries already observed).<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">.<\/p>\n<p style=\"text-align: justify;\">Let\u2019s concentrate on the portion of curves from the interval [-4\u00a0;4] and put them together on a unique graph.<\/p>\n<p><a href=\"http:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func6.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-22\" alt=\"func6\" src=\"http:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func6-300x168.png\" width=\"300\" height=\"168\" srcset=\"https:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func6-300x168.png 300w, https:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func6.png 465w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>And then, if we add some colors \u2026<\/p>\n<p><a href=\"http:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func7.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-23\" alt=\"func7\" src=\"http:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func7-300x168.png\" width=\"300\" height=\"168\" srcset=\"https:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func7-300x168.png 300w, https:\/\/www.lovemaths.fr\/blog_en\/wp-content\/uploads\/2013\/03\/func7.png 465w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>Happy Easter!<\/p>\n<p>Source\u00a0: <a href=\"http:\/\/www.mathematische-basteleien.de\/eggcurves.htm\">http:\/\/www.mathematische-basteleien.de\/eggcurves.htm<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>what is this? \u00a0. What a funny question! We can first do a study of the two associated functions. \u00a0We are told that the domain of definition of both functions is ]-\u221e ;-17\/2[ U [-4\u00a0;4] and that the tables of variations are those on the left side (we can see here the differences, translated into [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,2],"tags":[],"class_list":["post-18","post","type-post","status-publish","format-standard","hentry","category-fun","category-high-school"],"_links":{"self":[{"href":"https:\/\/www.lovemaths.fr\/blog_en\/index.php?rest_route=\/wp\/v2\/posts\/18","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lovemaths.fr\/blog_en\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lovemaths.fr\/blog_en\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lovemaths.fr\/blog_en\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lovemaths.fr\/blog_en\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=18"}],"version-history":[{"count":33,"href":"https:\/\/www.lovemaths.fr\/blog_en\/index.php?rest_route=\/wp\/v2\/posts\/18\/revisions"}],"predecessor-version":[{"id":56,"href":"https:\/\/www.lovemaths.fr\/blog_en\/index.php?rest_route=\/wp\/v2\/posts\/18\/revisions\/56"}],"wp:attachment":[{"href":"https:\/\/www.lovemaths.fr\/blog_en\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=18"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lovemaths.fr\/blog_en\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=18"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lovemaths.fr\/blog_en\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=18"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}