1.1.1 The Word "Function"

No doubt you already know an answer to the big question — What's a function? — from your previous study of mathematics. In fact, we will use your prior knowledge as our starting point for discussion and refinement of this central concept. Of course, only you can provide that prior knowledge.

Activity 1

Somewhere that you can keep track of it, write your present answer to the big question. You may use definitions, examples, symbols, or whatever you think appropriate for explaining to someone else what a function is.

The word "function," like all the other words we shall use in this course, belongs to the English language. As such, it has a definition — or several. Here are several from the Merriam-Webster Online Dictionary.

Function: noun
Etymology: Latin function-, functio performance, from fungi to perform; probably akin to Sanskrit bhunkte he enjoys

1. : professional or official position : OCCUPATION
2. : the action for which a person or thing is specially fitted or used or for which a thing exists : PURPOSE
3. : any of a group of related actions contributing to a larger action; especially : the normal and specific contribution of a bodily part to the economy of a living organism
4. : an official or formal ceremony or social gathering

Do you see any point of contact between that dictionary definition and what you wrote in response to Activity 1? Perhaps not — and therein lies a fundamental difficulty in the study of mathematics. Math books and math teachers seem to use words from the English language, but often with meanings that seem arbitrary and unrelated to common usage. Our use is more closely related to an alternate definition:

Something closely related to another thing and dependent on it for its existence, value, or significance: Growth is a function of nutrition.

Note 1 – Source

If you wrote something like that, give yourself a pat on the back. If nothing you wrote looks like that, don't despair — by the end of this chapter we will have connected your prior experience with the concept of "function" as the word will be used in this course.

You may have noticed that the title of this chapter is not "Functions" but "Relationships." The key word in the alternate definition is "related," and we will establish our meaning for the word "function" within the more general context of relationships.

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Contents for Chapter 1