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.