Putting It Together: Linear Functions and Function Notation

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.

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:

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

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 $1$ Grandpa May $2$ Mindy, Edward May $3$ Jacob May $4$ Greta , Maureen May $5$ David May $6$ Professor McGonagall , January Jones May $7$ Travis May $8$ Shelley, Shannon, Kelvin May $9$ Brianne May $10$ Thomas, Monica May $11$ Fritz, Liam May $12$

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

Notice how some dates, like May $3$, 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.