# What is the origin of a function?

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

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, $f(x) = 3x+2 \$ tells us:

• The function f is a function of x.
• To evaluate the function at a certain number, replace the x with that number.
• Replacing x with that number in the right side of the function will produce the function's output for that certain input

Please feel free to post as many doubts on our discussion forum as you can.

All the best.