A piecewise function uses different rules on different intervals. Pick the piece whose condition the input actually satisfies. Functions in general are in ACT Math functions.
Read the condition before the formula
Suppose f(x) = x + 2 when x < 0, and f(x) = x² when x ≥ 0. Then f(−3) uses the first piece: −3 + 2 = −1. f(4) uses the second: 16. f(0) uses the second, because the condition is ≥, not >. Using the other formula because it looks simpler is the whole trap.
Where each piece is allowed to exist is a domain question, in domain and range.
Composition still goes inside out
If you need f(g(x)) and f is piecewise, compute g(x) first, then choose the piece for that result. Composition order is in function composition. The notation for either function is in function notation.
The bottom line
Find which interval holds the input. Use only that formula. Check the endpoint when the inequality is strict.
Start practicing
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