Piecewise notation intimidates on paper because it's three functions wearing one name. Desmos's curly-brace syntax turns it back into one graph you can tap.
The move: Type it with curly braces, then tap.
Why it works: Desmos draws each rule only on its own interval, so the piecewise function behaves like a single normal graph — evaluation and intersections included.
The pattern
- Type f(x) = {condition: rule, …}
- Graph it
- Evaluate or tap the piece you need
Worked example: f(x) = x + 3 when x < 2, and f(x) = 2x − 1 when x ≥ 2. What is f(2)?
- Type it with the curly brace — conditions before the colon.
f(x)=x<2:x+3,x ≥ 2:2x-1 - x = 2 belongs to the SECOND piece (the ≥ side): f(2) = 2(2) − 1 = 3. Type f(2) to confirm.
f(2)
Worked example 2: f(x) = −x when x < 0, and f(x) = x + 2 when x ≥ 0. What is f(−3)?
- Type the piecewise function.
f(x)=x<0:-x,x ≥ 0:x+2 - −3 is negative → first piece: f(−3) = −(−3) = 3. Confirm with f(−3).
f(-3)
Remember it on test day
Curly brace = one graph. That's the whole cue — say it when you see this question type and the steps follow.
When this isn't the move
Watch the boundary: which piece owns x = 2 depends on ≤ vs < — read the zones before trusting a tapped value.
Drill it until it's reflex
This move is one of Desvantage's 18 training modules: a plain-English lesson, a type-it-yourself walkthrough inside a live Desmos calculator, and a 100-question drill bank that deals ten fresh questions per round. The first two modules — plus the 12-question diagnostic — are free.