Piecewise Behavior Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

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

Solution

  1. 1
    x=−2x=-2: ∣−2−3∣+∣−2+1∣=∣−5∣+∣−1∣=5+1=6|-2-3|+|-2+1| = |-5|+|-1| = 5+1 = 6.
  2. 2
    x=1x=1: ∣1−3∣+∣1+1∣=2+2=4|1-3|+|1+1| = 2+2 = 4. x=5x=5: ∣5−3∣+∣5+1∣=2+6=8|5-3|+|5+1| = 2+6 = 8.

Answer

66, 44, 88 for x=−2,1,5x=-2, 1, 5 respectively
Evaluating absolute value expressions requires computing each term independently, determining the sign of the contents, and applying the definition. No case analysis needed for specific numerical inputs.

About Piecewise Behavior

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.

Learn more about Piecewise Behavior →

More Piecewise Behavior Examples

Example 1 easy

Write [formula] as an explicit piecewise function, evaluate [formula], [formula], and [formula], and

Example 2 medium

Solve the equation [formula] and the inequality [formula].

Example 4 hard

Express [formula] as a piecewise function (without absolute value bars) and identify where [formula]

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