Calc01_5 - 1.5 Functions and Logarithms Golden Gate Bridge...

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1.5 Functions and Logarithms Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2004 Golden Gate Bridge San Francisco, CA
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A relation is a function if: for each x there is one and only one y . A relation is a one-to-one if also: for each y there is one and only one x . In other words, a function is one-to-one on domain D if: ( 29 ( 29 f a f b whenever a b
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To be one-to-one, a function must pass the horizontal line test as well as the vertical line test. 3 1 2 y x = 2 1 2 y x = 2 x y = one-to-one not one-to-one not a function (also not one-to-one)
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Inverse functions: ( 29 1 1 2 f x x = + Given an x value, we can find a y value. 1 1 2 y x = + 1 1 2 y x - = 2 2 y x - = 2 2 x y = - Switch x and y : 2 2 y x = - ( 29 1 2 2 f x x - = - (eff inverse of x) Inverse functions are reflections about y = x . Solve for x :
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example 3: ( 29 2 f x x = 0 x Graph: ( 29 f x ( 29 1 f x - y x = for 0 x a parametrically: 2 1 1 : 0 f x t y t t = = 1 2 2 2 : f x t y t - = = 3 3 : y x x t y t = = = Y= WINDOW GRAPH
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GRAPH WINDOW example 3: ( 29 2 f x x = 0 x Graph: ( 29 f x ( 29 1 f x - y x = for 0
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