Why learn about functions and function notation?

It is Joan’s birthday, and she has decided to spend it with her friend Hazel. To celebrate, Hazel and Joan are heading to the city to see a new art exhibit of paintings by artists from the Northwest School. Joan is really excited to check out some pieces by Mark Tobey, her favorite artist.

As Joan and Hazel are driving to the city, Joan wonders how many other people in the world share her birthday. Joan remembers following some click-bait on the internet about birthdays and reading that September 16 is the most common birthday in the U.S., while December 25 and February 29 are the least common. ^[1].

She considers how interesting it is that each person only has one unique birthday, while many people might share the same day of birth, and doodles the following drawing on the back of an envelope.

Without realizing it, Joan has discovered the definition of a mathematical function. 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. If you were to go backward, though, you could have many people with the same birthday.

In this module we will introduce the definition of a function and the formal mathematical notation that is used to express functions. You will see that there are many mathematical relationships that you are already familiar with that fit the definition of a function. Probably the most familiar of these relationships are linear equations for straight lines.