{"id":4420,"date":"2016-10-03T21:05:52","date_gmt":"2016-10-03T21:05:52","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&p=4420"},"modified":"2017-07-27T17:00:32","modified_gmt":"2017-07-27T17:00:32","slug":"conclusion-5","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/chapter\/conclusion-5\/","title":{"raw":"Putting It Together: Functions and Function Notation","rendered":"Putting It Together: Functions and Function Notation"},"content":{"raw":"

Put it Together<\/h2>\r\nAt the beginning of the module, we left Joan pondering the idea that even though\u00a0her birthday is unique to her - we all have only one birthday - each possible birth date is not unique with respect to how many people have it. In other words, Joan has one birthday, but many people were also born on that day.\r\n\r\n\"four\r\n\r\nWe proposed the following idea:\r\n\r\nThink of\u00a0each individual person on the earth as a variable, p. Now imagine that all the birthdays are a function, B. For each individual person you place in the Birthday function, you will get out one unique birthday for that person.\r\n\r\nAs we have shown in this module, we can write this relationship as a function in the following way:\r\n\r\n[latex]B(p)=\\text{Person p's birthdate}[\/latex]\r\n\r\nJoan decides to survey people\u00a0so she can make a plot of\u00a0her birthday function. She started surveying people at the art opening she and Hazel went to, but didn't collect enough data. So, she also asks\u00a0her Facebook friends (of which she has many) to send their birthdays. Some of the data she collected for May is in the table below.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Name<\/td>\r\nBirthday<\/td>\r\n<\/tr>\r\n<\/thead>\r\n
\u00a0Homer<\/td>\r\nMay 1<\/td>\r\n<\/tr>\r\n
Grandpa<\/td>\r\nMay 2<\/td>\r\n<\/tr>\r\n
Mindy, Edward<\/td>\r\nMay 3<\/td>\r\n<\/tr>\r\n
Jacob<\/td>\r\nMay 4<\/td>\r\n<\/tr>\r\n
Greta , Maureen<\/td>\r\nMay 5<\/td>\r\n<\/tr>\r\n
\u00a0David<\/td>\r\nMay 6<\/td>\r\n<\/tr>\r\n
Professor McGonagall , January Jones<\/td>\r\nMay 7<\/td>\r\n<\/tr>\r\n
\u00a0Travis<\/td>\r\nMay 8<\/td>\r\n<\/tr>\r\n
\u00a0Shelley, Shannon, Kelvin<\/td>\r\nMay 9<\/td>\r\n<\/tr>\r\n
Brianne<\/td>\r\nMay 10<\/td>\r\n<\/tr>\r\n
Thomas, Monica<\/td>\r\nMay 11<\/td>\r\n<\/tr>\r\n
Fritz, Liam<\/td>\r\nMay 12<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nJoan then plotted the data with Excel and got the following graph:\r\n\r\n[caption id=\"attachment_4091\" align=\"aligncenter\" width=\"471\"]\"Birthday Birthday Data for May[\/caption]\r\n\r\nNotice how some dates, like May 3, have multiple people associated with them. \u00a0On the other hand, all the people have only one birthdate that they are associated with.\r\n\r\nFunctions are a very useful tool in mathematics, and we will continue to use them throughout the rest of this course. \u00a0You will most definitely study more functions if you take more math courses in the future.","rendered":"

Put it Together<\/h2>\n

At the beginning of the module, we left Joan pondering the idea that even though\u00a0her birthday is unique to her – we all have only one birthday – each possible birth date is not unique with respect to how many people have it. In other words, Joan has one birthday, but many people were also born on that day.<\/p>\n

\"four<\/p>\n

We proposed the following idea:<\/p>\n

Think of\u00a0each individual person on the earth as a variable, p. Now imagine that all the birthdays are a function, B. For each individual person you place in the Birthday function, you will get out one unique birthday for that person.<\/p>\n

As we have shown in this module, we can write this relationship as a function in the following way:<\/p>\n

[latex]B(p)=\\text{Person p's birthdate}[\/latex]<\/p>\n

Joan decides to survey people\u00a0so she can make a plot of\u00a0her birthday function. She started surveying people at the art opening she and Hazel went to, but didn’t collect enough data. So, she also asks\u00a0her Facebook friends (of which she has many) to send their birthdays. Some of the data she collected for May is in the table below.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Name<\/td>\nBirthday<\/td>\n<\/tr>\n<\/thead>\n
\u00a0Homer<\/td>\nMay 1<\/td>\n<\/tr>\n
Grandpa<\/td>\nMay 2<\/td>\n<\/tr>\n
Mindy, Edward<\/td>\nMay 3<\/td>\n<\/tr>\n
Jacob<\/td>\nMay 4<\/td>\n<\/tr>\n
Greta , Maureen<\/td>\nMay 5<\/td>\n<\/tr>\n
\u00a0David<\/td>\nMay 6<\/td>\n<\/tr>\n
Professor McGonagall , January Jones<\/td>\nMay 7<\/td>\n<\/tr>\n
\u00a0Travis<\/td>\nMay 8<\/td>\n<\/tr>\n
\u00a0Shelley, Shannon, Kelvin<\/td>\nMay 9<\/td>\n<\/tr>\n
Brianne<\/td>\nMay 10<\/td>\n<\/tr>\n
Thomas, Monica<\/td>\nMay 11<\/td>\n<\/tr>\n
Fritz, Liam<\/td>\nMay 12<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Joan then plotted the data with Excel and got the following graph:<\/p>\n

\"Birthday<\/p>\n

Birthday Data for May<\/p>\n<\/div>\n

Notice how some dates, like May 3, have multiple people associated with them. \u00a0On the other hand, all the people have only one birthdate that they are associated with.<\/p>\n

Functions are a very useful tool in mathematics, and we will continue to use them throughout the rest of this course. \u00a0You will most definitely study more functions if you take more math courses in the future.<\/p>\n","protected":false},"author":21,"menu_order":5,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4420","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4420\/revisions"}],"predecessor-version":[{"id":4542,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4420\/revisions\/4542"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4420\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/wp\/v2\/media?parent=4420"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=4420"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/wp\/v2\/contributor?post=4420"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/wp\/v2\/license?post=4420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}