Traffic Light Functions

Algebra 2 · Axiom Academy

One intersection, four rules — discover how a piecewise function decides how long the green light lasts, hour by hour. A traffic light doesn't run on one rule all day — 7 AM gets a different rule than 2 PM , and 11 PM gets a different rule still. Drag through the hours — or watch the whole day run — and see the green-light rule change with the clock. The N–S green time is a piecewise function of the hour: one formula, four pieces, each owning its own slice of the day. Scrub to see which piece is active, then confirm what makes it piecewise. Why is this called a piecewise function? Compare a single fixed timing against the adaptive piecewise schedule across the same day — then see where else this kind of rule shows up. This same idea prices the real world: Electricity rates — different prices for peak vs. off-peak hours Tax brackets — different rates for different income ranges Shipping costs — tiered pricing based on weight Parking fees — rates that vary throughout the day Four ideas from this whole module: Multiple rules — different formulas apply to different parts of the domain (the input values). Each piece has a domain — the domain specifies exactly when each rule applies (like 7 t < 9 for morning rush). Built for conditional situations — when real-world behavior changes based on conditions, piecewise functions model it perfectly.

This is the written version of the interactive lesson above. See the full Algebra 2 course.