Concept

Identity Function

An identity function is a function whose output is equal to its input across its entire domain. The identity function can be represented by the following formula.

$f (x) = x$

For every

x -

value, the corresponding

y -

value is equal to that

x -

value, so the points on the graph of

f

are in the form

(x, x)

for all real numbers

x .

This results in a diagonal straight line passing through the origin.

Function f(x)=x and a point on the graph with its coordinates shown

The identity function is a building block for all linear functions. Any linear function has the form

f (x) = m x + b,

where

m

is the slope of the line and

b

is the

y -

intercept. Then the identity function

f (x) = x

is the simplest linear function with

m = 1

and

b = 0 .

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