Practice Piecewise Behavior in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Piecewise behavior refers to a function that exhibits qualitatively different characteristics in different regions of its domain, like having a different slope or curvature in each region.

Think of the behavior as shifting gears — the function follows one rule until it hits a boundary, then switches to a different rule for the next region.

Example 1

easy
Write |x| as an explicit piecewise function, evaluate |-4|, |0|, and |7|, and sketch its graph.

Example 2

medium
Solve the equation |2x - 5| = 7 and the inequality |2x - 5| < 7.

Example 3

easy
Simplify |x-3| + |x+1| for x = -2, x = 1, and x = 5.

Example 4

hard
Express f(x) = |x^2 - 4| as a piecewise function (without absolute value bars) and identify where f(x) = 0.
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