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What is the origin of a function?
Dear paul,
To provide the classical understanding of functions, think of a function as a kind of machine. You feed the machine raw materials, and the machine changes the raw materials into a finished product based on a specific set of instructions. The kinds of functions we consider here, for the most part, take in a real number, change it in a formulaic way, and give out a real number (possibly the same as the one it took in). Think of this as an input-output machine; you give the function an input, and it gives you an output. For example, the squaring function takes the input 4 and gives the output value 16. The same squaring function takes the input − 1 and gives the output value 1.
A function is usually written as f, g, or something similar - although it doesn't have to be. A function is always defined as "of a variable" which tells us what to replace in the formula for the function.
For example, tells us:
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