### Modeling with Functions

Prior to the start of the Spring 2007 semester, Gateway Community College advertised for a "model" for an art drawing class.

MathBabbler noticed that cluster one of chapter one of the "Mathematics in Action" textbook was titled "Modeling with Functions."

Why would a model need any functions?

At a minimum, the Gateway model would need bodily functions (i.e. they need to drink, eat, sleep, etc.), but it is difficult to explain the phrase "modeling with functions" because the words model and function both have multiple definitions. The phrase "modeling with functions" uses the mathematical forms of the words.

The following was copied from the 9th edition of a textbook titled "Calculus" by Varberg, Purcell and Rigdon.

```   "It is important to keep in mind that all models
such as this are simplifications of reality. (That
is why they are called 'models'.)  Although such
models are inherently simplifications of reality,
many of them are still useful for prediction."
```

The "models such as this" was in reference to the textbook stating: "Trigonometric functions can be used to model a number of physical phenomena, including daily tide levels and yearly predictions."

In math world, a function is "a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set."

function. (2008). In Merriam-Webster Online Dictionary.
Retrieved August 23, 2008, from
http://www.merriam-webster.com/dictionary/function

Also in math world, a model is "a system of postulates, data, and inferences presented as a mathematical description of an entity or state of affairs."

model. (2008). In Merriam-Webster Online Dictionary.
Retrieved August 23, 2008, from
http://www.merriam-webster.com/dictionary/model

To be completed...

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 28 January 2007