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Function Notation . . . f(x)
. . .

Shown and Explained

Math - Symbol for Function of x

Function Notation . . . f(x)

Background - why the Function Notation symbol is used . . .

Symbols are used as a concise way of giving lengthy instructions

related to numbers and logic.

Math Symbols are a communication tool. Symbols are an invention which is used to eliminate the need to write long, plain language instructions to describe calculations and other processes.

The most valuable, most frequently used Symbols in
mathematics . . .

The most important, most frequently used Miscellaneous symbols are listed below.

Math - Symbol for Function of x Math Notation for the "Function" of x -

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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.