Piecewise Functions - Precalculus & Trigonometry Step by Step

Evaluate a piecewise function f(x) = {x² if x < 2; 3x-2 if x ≥ 2} at three different input values, applying the correct piece each time.

For f(x) = x² if x < 2; 3x - 2 if x ≥ 2: f(1): since 1 < 2, use x²: f(1) = 1² = 1. f(2): since 2 ≥ 2, use 3x - 2: f(2) = 3(2) - 2 = 4. f(3): since 3 ≥ 2, use 3x - 2: f(3) = 3(3) - 2 = 7.

piecewise-functions A piecewise function uses different formulas on different parts of its domain. To evaluate, first determine which piece applies to the input value, then use that formula.

Example

Choose the matching piece for each input, then evaluate.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

f(x)=\begin{cases}x^{ 2 }&x< 2 \\ 3x - 2 &x\ge 2 \end{cases}

Step 2 — Use first piece

Since 1 is less than 2, use x squared: 1 squared is 1.

f( 1 )= 1 ^{ 2 }= \hl{1}

Step 3 — Use second piece at boundary

Since 2 is at least 2, use the linear piece; the value is 4.

f( 2 )= 3 ( 2 )- 2 = \hl{4}

Step 4 — Use second piece

Since 3 is at least 2, use the linear piece; the value is 7.

f( 3 )= 3 ( 3 )- 2 = \hl{7}