AdvancedProAdvanced Functions
Piecewise Function
f(x) = {...}
Overview
A piecewise function uses different formulas on different intervals. Continuity depends on the boundary values.
Domain
Depends on intervals
Range
Depends on pieces
Symmetry
Depends on definition
Key Properties
1
Different rules for different x ranges
2
Check continuity at each boundary
3
Can model real-world step changes
4
Derivative may not exist at boundaries
Key Insight
To check continuity at a boundary x=a: left limit, right limit, and f(a) must all be equal.
Visualize Piecewise Function
Interact with the graph, adjust parameters, and see how the function behaves in real time.