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.

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:

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

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

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

Birthday Data for May. The horizontal axis is labeled name, and the vertical axis is labeled birthday. The graph displays the data from the previous table from Joan's survey. For each person, there is exactly one birthdate, however, for each birth date there can be more than one person.

Notice how some dates, like May [latex]3[/latex], 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.