Piecewise Function Math Example 3

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

Example 3

easy
Given g(x)={−xx<−1x2−1≤x≤25x>2g(x) = \begin{cases} -x & x < -1 \\ x^2 & -1 \leq x \leq 2 \\ 5 & x > 2 \end{cases}, evaluate g(−2)g(-2), g(1)g(1), and g(3)g(3).

Solution

  1. 1
    g(−2)g(-2): −2<−1-2 < -1, so g(−2)=−(−2)=2g(-2) = -(-2) = 2.
  2. 2
    g(1)g(1): −1≤1≤2-1 \leq 1 \leq 2, so g(1)=12=1g(1) = 1^2 = 1. g(3)g(3): 3>23 > 2, so g(3)=5g(3) = 5.

Answer

g(−2)=2,  g(1)=1,  g(3)=5g(-2)=2,\; g(1)=1,\; g(3)=5
Each input value must be tested against the boundary conditions in the piecewise definition. Once the correct interval is identified, simply apply the associated rule.

About Piecewise Function

A piecewise function is defined by different formulas on different non-overlapping intervals of its domain, with the applicable formula determined by the input value.

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More Piecewise Function Examples

Example 1 easy

Evaluate [formula] at [formula], [formula], and [formula].

Example 2 medium

Determine whether [formula] is continuous at [formula].

Example 4 hard

Find the value of [formula] so that [formula] is continuous at [formula].

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