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Study Guides > Intermediate Algebra

Putting it Together: Functions

At the beginning of the module, we left Joan pondering the idea that even though her 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. four ovals in a column on the righ hand side of the page the top one says random person 1 and has an arrow point to it from an oval on the right hand side of the page that says my birthday. The next oval in the column on the left says random person two and also has an arrow pointing to it from the birthday oval on the right. the next oval in the column on the left say me and has an arrow pointing from it to the birthday oval. The bottom oval on the left also has an arrow pointing to it from tthe birthday oval. We proposed the following idea: Think of each 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. As we have shown in this module, we can write this relationship as a function in the following way:

B(p)=Person p’s birthdateB(p)=\text{Person p's birthdate}

Joan decides to survey people so she can make a plot of her birthday function. She asks her Facebook friends (of which she has many) to send their birthdays. Some of the data she collected for May is in the table below.

Name Birthday
 Homer May 11
Grandpa May 22
Mindy, Edward May 33
Jacob May 44
Greta , Maureen  May 55
 David May 66
Professor McGonagall , January Jones May 77
 Travis May 88
 Shelley, Shannon, Kelvin May 99
Brianne May 1010
Thomas, Monica May 1111
Fritz, Liam May 1212

Joan then plotted the data with Excel and got the following graph:

Birthday Data for May Birthday Data for May

Notice how some dates, like May 33, have multiple people associated with them.  All the people, on the other hand, have only one birthdate that they are associated with.

Functions are a very useful tool in mathematics, and we will continue to use them throughout the rest of this course.  You will most definitely study more functions if you take more math courses in the future.

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