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Piecewise-defined Functions ½ x – 2, x > 2 f(x) =f(x) =3, x = 1 –2x + 3, –2 x < 1 Ex. 1: x y h/d x y h/d y x O x – 1, x < –3 f(x) =f(x) = x – 3, x = 4 –2 / 3 x + 2, –3 x < 3 Ex. 2: x y h/d x y h/d y x O Domain: __________Range: ___________Evaluate: a) f(–1) = b) f(3) =c) f(4) = Domain: __________Range: ___________Evaluate: a) f0) = b) f(1) =c) f(2) =

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Piecewise-defined Functions (contd) –3 / 2 x + 4, x > 2 f(x) =f(x) = 2x – 1, –3 < x 2 Ex. 3: x y h/d x y h/d y x O |x|, –3 x < 1 f(x) =f(x) = x – 5, x = 3 3, 1 x < 2 Ex. 4: x y h/d x y h/d y x O Evaluate: a) f(–2) = b) f(2) =c) f(4) =Domain: __________Range: ___________ Domain: __________Range: ___________Evaluate: a) f(–3) = b) f(1.5) =c) f(3) =

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Piecewise-defined Functions (contd) x, x > 1 f(x) =f(x) = –2x – 7, x –2 Ex. 5: x y h/d x y h/d y x O Domain: __________Range: ___________Evaluate: a) f(4) = b) f(1) = c) f(–3) = f(x) =f(x) = Ex. 6: y x O x 2, –2 < x 1 x y h/d Domain: __________Range: ___________Increasing: __________Decreasing: __________

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Piecewise-defined Functions (contd) f(x) =f(x) = Ex. 7: y x O f(x) =f(x) = Ex. 8: y x O Domain: __________Range: ___________Increasing: __________Decreasing: __________ Domain: __________Range: ___________Increasing: __________Decreasing: __________

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Increasing & Decreasing Functions A function f is increasing on an interval if, for any x 1 and x 2, in the interval, x 1 < x 2 implies f(x 1 ) < f(x 2.

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