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One-to-One Functions Functions with Inverses

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8/10/2013 One-to-One Functions 2 Definition A function f is a one-to-one function if no two ordered pairs of f have the same second component Note: One-to-one is often written as 1-1

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8/10/2013 One-to-One Functions 3 1-1 Examples: 1. f = { (1, 3), (2, 5), (3, 2), (7, 1) } 2. g = { (1, 3), (2, 5), (3, 6), (7, 3) } 3. h = { (5, 3), (2, 9), (5, 6), (8, 7) } 4. f(x) = (x – 4) 2 + 7 5. g(x) = x + 1 6. f(x) = |x + 1| One-to-One Functions NOT 1-1 NOT a function WHY ?

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8/10/2013 One-to-One Functions 4 Horizontal Line Test No horizontal line intersects the graph of a 1-1 function more than once Examples x y(x) x ● ● ● 1-1 function Not 1-1

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8/10/2013 One-to-One Functions 5 Horizontal Line Test No horizontal line intersects the graph of a 1-1 function more than once More Examples x y(x) x x ●● ● ● ● ● ● ● NOT a function ! Not 1-1

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8/10/2013 One-to-One Functions 6 Think about it !

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