IntroPolynomial Functions

Linear Function

f(x) = ax + b

Overview

A linear function has a constant rate of change. Its graph is a straight line.

Domain

(-∞, +∞)

Range

(-∞, +∞)

Symmetry

Neither (unless b = 0)

Key Properties

1

a = slope (rate of change)

2

b = y-intercept

3

Constant first derivative

4

No extrema (unless a = 0)

Key Insight

The slope a tells you how steep the line is. Positive a → rising, negative a → falling.

Visualize Linear Function

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

Open Visualizer