Graph and evaluate piecewise-defined functions with up to 3 pieces. Identify domain, range, and continuity, evaluate at any x value, and see open/closed boundary circles on the graph.
f(x) = { expr₁, condition₁ ; expr₂, condition₂ ; … }
A piecewise function is defined by different expressions on different parts of its domain. Each "piece" has its own formula and a condition specifying which x values it applies to.
Example: the absolute value function is piecewise — it equals −x when x < 0, and x when x ≥ 0.
Pieces must collectively cover every x in the domain with no overlaps (each x belongs to exactly one piece).
lim x→c⁻ f(x) = lim x→c⁺ f(x) = f(c)
A piecewise function is continuous at x = c if the left-hand limit, right-hand limit, and the function value all agree. If any differ, there is a discontinuity.
Types of discontinuities:
This tool checks each internal boundary by computing both one-sided limits numerically.
A live tutor can walk you through defining pieces, graphing them by hand, and checking continuity — step by step.