Objects

In this view, functions are objects. They consist of pieces. They have features, characteristics, and attributes. As objects, they can be examined, measured, and involved in operations.

We can also link these objects as a chain by gluing together the range of one function with the domain of another function. In this way, we produce a new function called the composition.

Machines

We can also view functions as machines, so-called black-boxes. They take input from the domain, process it, and return an output from the range. For each input, the process produces exactly one output.

This output could easily be fed into another function, processed by this second function, and producing a final output.

Before chaining whole functions together to form new functions, in this section, we will simply follow individual numbers through the chaining process and see where they end up.

Learninng Outcomes

In this section, students will

• trace values of one function as domain value for another.