Algebra I – Tuesday

 Algebra I Learning Targets for the day:

I can determine if a relation is a function.

I can identify the domain and range of a function.

Agenda:

New Learning Groups were assigned.
Students read "What is a Function" attached below.
Whole class discussion of reading sample - taking notes as we define domain / range, etc. (see flipcharts below)
Assignment:  Skills Practice pages 365 Vocabulary #1-9, Problem Set #1-23 odds.

What is a Function? 

 (www.azstarnet.com/~maxinfo/func.htm)  – this article has been used for 14+ years and may not be accessible through internet anymore.

A function is a special type of relation between the members of a set called the domain and the members of another set called the range. To each member of the domain, a function assigns at most one member of the range.

Typically, we can think of the domain supplying the inputs and the range supplying the outputs for a function. The function itself can be defined in many ways through a table, a graph, an equation, or a verbal description. In this document we will concentrate on verbal descriptions and the definition of functions.

The roles of the domain and range are often interchanged by students. This is easily rectified by examining the MOO function:

The inputs to the MOO function are grasses in Arizona. The outputs are meadow muffins.

Where do you find these inputs? In the cow’s domain of course.

Where do you find the outputs? Home, home on the range of course.

A cow takes its inputs of grass from its domain and leaves its outputs of meadow muffins on the range.

 

Now that you understand the relationship between the domain and range, what types of things can be in them? In other words, what can the inputs and outputs for a function consist of?

Depending on the function, the domain and range can be almost anything. For example, consider a function which assigns social security numbers to each resident of the United States. The residents form the domain and the numbers form the range. You can think of the function as a computer in Washington which takes inputs of people and outputs their social security numbers. The function is the process or rule which connects people and their numbers, not the people or numbers themselves.

The grocery scanner in a supermarket can also be thought of as a function. In this case the domain is made up of grocery items in the store and the range is the corresponding prices. This correspondence is a function since each grocery item is assigned only one price.

These two examples give you the impression that every relation is a function, but this is not the case. Let’s consider a device that works in a manner opposite to the grocery scanner. As inputs, this device takes prices. As outputs, this device yields grocery items. These are the same domain and range we had before, but in reverse. Is this a function? To be a function each member of the domain (price) must correspond to, at most, one member of the range (grocery item). This is obviously not true since many grocery items have the same price so this device can’t be thought of as a function.

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