Piecewise functions
Evaluate piecewise functions by choosing the correct rule for a given input.
Objective
Evaluate piecewise functions by choosing the correct rule for a given input.
What it means
A piecewise function is defined by different expressions over different intervals of its domain. To evaluate it at a given x, find the interval that contains that x and use the matching rule.
Key terms
- Piece
- One of the sub-functions that applies over a specific interval.
- Domain restriction
- The interval condition (like x < 2) that tells you which piece to use.
Rules to remember
- Check which interval the input value falls into.
- Substitute the input into only that piece's formula.
- Boundary points use whichever inequality includes them (≤ or ≥).
Step by step
- 1Locate the inputFind which condition (interval) the given x-value satisfies.
- 2Select the ruleUse only the formula attached to that condition.
- 3EvaluateSubstitute x into that formula and simplify.
Common mistakes
- Using the wrong piece when the input equals a boundary value.
- Plugging the input into every piece instead of just one.
Tips
- Underline the boundary inequality symbols so you know which piece 'owns' the boundary point.
- Double check by confirming the input truly satisfies the condition you chose.