Standard notation and function notation are used in almost the exact same way. The

y

variable in standard notation and

f (x)

in function notation are basically the same thing. In standard notation,

x

and

y

are the input and output respectively, while in function notation, if

x

is the input, then

f (x)

is the output. The main difference comes from how we write specific inputs and outputs.

Standard Notation : y = 2 x + 5 Function Notation : f (x) = 2 x + 5

If we take the given example equations and want to find the output when

x = 3,

we have to notate things as shown below.

Standard Notation : Evaluate when x = 3 . Function Notation : f (3) = ?

When we want to show the solution, we write the following.

Standard Notation : y = 11 Function Notation : f (3) = 11

If we assume that we didn't know the function or the value of

x

, when looking at the solution in standard notation, we can only see what the value for

y

is

11

at some given point. However, in function notation, whether we know the function or not, we know that the function gives an output of

11

when the input is

3 .

Exercise