IntroPolynomial Functions

Identity Function

f(x) = x

Overview

The identity function returns exactly its input. It's the simplest linear function.

Domain

(-∞, +∞)

Range

(-∞, +∞)

Symmetry

Odd (rotational symmetry about origin)

Key Properties

1

Slope = 1 everywhere

2

Passes through origin

3

Odd function

4

f(f(x)) = x (self-inverse)

Key Insight

The identity function is its own inverse — applying it twice gets you back to where you started.

Visualize Identity Function

Interact with the graph, adjust parameters, and see how the function behaves in real time.

Open Visualizer