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P.3: Part 2 Functions and their Graphs

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Transformations on Parent Functions: y = f(x): Parent Functions y = f(x – c) y = f(x + c) y = f(x) – c y = f(x) + c y = -f(x) y = f(-x) y = -f(-x) y = df(x) y = f(dx)

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Describe what would happen to the parent function and sketch graphs of each: f(x) = 3(x + 2) 2 – 1

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Describe what would happen to the parent function and sketch graphs of each: f(x) = -3sin(x + π/2) + 2

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Composite Functions: f(x) = x 2 – 1, g(x) = cos x Find f ° gFind g ° f Give the domain of each composite function.

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Composite Functions: f(x) =, g(x) = x 2 + 1 Find the following: f(g(0)) = g(f(0)) = f(g(1)) = g(f(1)) = f(g(x)) =

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Decide if each function is even, odd, or neither. f(x) = 4 – x 2 p(x) = x cos x

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