Lesson 2 a Function Is Predictable This Lesson Will Introduce the Additional Vocabulary

Lesson 2 – A Function is Predictable – This lesson will introduce the additional vocabulary of input and output ,_____ is a function of _____, and domain and range, and will begin to seed the idea of one-to-one correspondence.

Part 1 - Class discussion that a relationship in which the second variable is predictable based on the first variable is a function.

Ex: (Could actually get an electric juicer and fruit to demonstrate…)

If you put oranges into a juicer, you get out orange juice.

If you put apples into a juicer, you get out apple juice.

If you put grapefruit into a juicer, you get out grapefruit juice.

You can predict the kind of juice you will have based on the kind of fruit you put

into the juicer.

The domain of the function (the juicer) is fruit; the range of the function is fruit juice.

If you put oranges into the juicer, you cannot get anything but orange juice out.

The output (kind of fruit juice) depends on the input (kind of fruit).

The kind of juice is a function of the kind of fruit.

Part 2 – Students will practice identifying functional relationships between two variables.

(See A Function is Predictable Worksheet)

Be sure to point out to students that some pairs of variables may have a functional relationship if the first variable is considered to be the input and the second variable is considered to be the output, but the opposite is not true. For example, Social Security Number, First Name is a function if we consider Social Security Number to be the input, because each Social Security Number is assigned to only one person. However, if we take First Name as the input and Social Security Number as the output, it is no longer a function because there are many people with the same first name who all have different social security numbers.

Be sure to emphasize to students that it is also important to consider domains when identifying functions. For example, at one high school, Locker Number, Student may be a function if no students at that school share lockers. However, at another school, students may share lockers, and this relationship would no longer be a function. Similarly, a relation like First Name, Student ID number could be a function inside a particular classroom, for example, but not on a larger scale like the entire freshman class.