## Why Learn About Functions and Function Notation?

It is Joan’s birthday, and she has decided to spend it with her friend Hazel. They are going to the city to see an art exhibit of paintings by artists from the Northwest School, including some pieces by Mark Tobey, her favorite artist. Joan has been looking forward to it for a long time.

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 it is interesting that each person only has one unique birthday, while many people might share the same birthday, 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 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.