Function Notation . . . f(x)
. . .
Shown and Explained
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 the "Function of x" -
The Function Notation f(x) means two things:
f(x) literally means that the value of f(x) depends upon the value of x
And . . .
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).
, 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.
, the following relation is not
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.