Expressions & functions09 / 68

Piecewise rules & restrictions

A piecewise function uses different formulas on different parts of its domain.

Find it

Expressions; structured piecewise editor in Braille input

Try it step by step

Write each condition followed by its value inside braces.
Separate branches with commas. Check the value at the boundary from both sides.
Use a final unrestricted branch only when you want a fallback value.
For accessible structured editing, use the piecewise branch editor in Braille input.

Each card is one input. For definitions, enter the cards in order. Formula-only cards belong in the tool described above.

A line on the left and a parabola on the right.

The square-root domain still applies, along with the added upper limit.

Condition: Decides when a branch applies, for example .
Branch value: The formula used when its condition is true.
Undefined regions: A point outside all applicable branches has no value unless you provide a fallback.
Boundary behavior: A jump, corner or excluded point may make a derivative undefined. Do not assume a connecting stroke proves continuity.