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Function Notation . . . f(x)
. . .
Shown and Explained

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Background - why a symbol for Function Notation is used. . .

Symbols are a concise way of giving lengthy instructions related to numbers and logic.

Symbols are an invention, not a discovery. They are a communication tool. Symbols are used to eliminate the need to write long, plain language instructions to describe calculations and other processes. 




The most valuable, most frequently used Math Symbols . . .

          The most important, most frequently used Miscellaneous symbols 
          are listed below.
Math - Symbol for Funciton of x Math Symbol for the "Function of x" -
The Function Notation f(x) means two things: (1) f(x) literally means that the value of f(x) depends upon the value of x And . . . (2) For every value of x, there is only one unique value f(x). f(x) is often used interchangeably with y.

Most of the time this is OK, but y is not the same as f(x).

f(x) is a function. f(x) always satisfies both of the criteria listed as (1) and (2), shown above.

Y may or may not represent a function. It may only satisfy the criteria listed as (1).
Example 1: f(x) , function of x (can be used interchangeably with the y
in this example) y = x + 1 f(x) = x + 1 if x = 4 y = 4 + 1 y = 5 f(4) = 4 + 1 f(4) = 5 Note: both y and f(x) represent a function. Both notations satisfy the criteria for (1) and (2) above. Note: both y
and f(x) = 5.
Example 2: y , the following relation is not a function Not a Function Not a Function Note: there are two values of y for every value of x. A function can have only one value of y for each value of x. Therefore, this is not a function.


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