Interactive resource
Piecewise Functions: Different Rules on Each Side
Functions. Move the breakpoint and left/right slopes to see continuity and corners. Free interactive GeoGebra resource — adjust parameters in the browser.
Overview
Piecewise functions use different formulas on different intervals. Matching values keep continuity; different slopes can create a corner.
Explanation
A piecewise function uses different expressions on different intervals.
Matching values at the breakpoint gives continuity; different slopes can create a corner.
Graph each piece after locating the breakpoint.
How to use
- Open the piecewise scene.
- Move the breakpoint.
- Adjust left and right slopes.
- Decide whether the join is smooth.
Discussion
If slopes match, is the graph necessarily a single linear piece globally?
Knowledge points
FAQ
Is this exam-relevant?
Evaluating and graphing piecewise functions is common; this builds visual fluency.
Is this tool free?
Yes. It runs in the browser with no install.
Good for class demos?
Yes — project it and ask what changes when you drag a parameter.
How do I write the formula afterward?
Open the equation editor or symbol sheet and copy a clean expression.